Finding the Area of Triangles 6.3.1.2 Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.

I can… Determine the area of triangles Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Area of a Triangle = ½ Base × Height Finding the Area of Triangles Area of a Triangle = ½ Base × Height Height We already know how to find the area of a rectangle. In this lesson we will learn how to see, understand, and find the area of a triangle. The area of a triangle can be found using the formula one half of the base times the height. The base is the horizontal width, usually at the bottom of the triangle. The height is normally the vertical distance from the base to the highest point of the triangle. Base The height is normally the vertical distance from the base to the highest point of the triangle. In this lesson we will learn how to see, understand, and find the area of a triangle. We already know how to find the area of a rectangle. The area of a triangle can be found using the formula one half of the base times the height. The base is the horizontal width, usually at the bottom of the triangle.

Finding the Area of Triangles 8 square units Let’s begin with this triangle. We’ll use a grid to help us see square units. Now, we can count the number of whole square units. 1 2 3 4 5 6. We can also add on the half units that remain. 6 ½ 7 7 ½ 8 The area of this triangle is 8 square units. 7 7 ½ The area of this triangle is 8 square units. 6 ½ 8 6. We can also add on the half units that remain. 1 We’ll use a grid to help us see square units. Now, we can count the number of whole square units. 2 3 5 4 Let’s begin with this triangle.

Finding the Area of Triangles 8 square units We can also decompose this triangle into smaller shapes and rearrange them to see the area. Let’s move this half triangle here … … and this half triangle here. Now, how many whole squares can we see? 8. There are 8 square units. 8. There are 8 square units. Let’s move this half triangle here … … and this half triangle here. Now, how many whole squares can we see? We can also decompose this triangle into smaller shapes and rearrange them to see the area.

Finding the Area of Triangles 8 square units So, the area of this triangle is 8 square units. So, the area of this triangle is 8 square units.

Finding the Area of Triangles 8 square units We can also decompose the triangle in other ways. Let’s move the top of the triangle to here. Again, we see 8 square units. Let’s move the top of the triangle to here. Again, we see 8 square units. We can also decompose the triangle in other ways.

Finding the Area of Triangles 8 square units So, the area of this triangle is 8 square units. So, the area of this triangle is 8 square units.

Finding the Area of Triangles 8 square units Now, here is the rectangle that contains our triangle. What is the area of the whole rectangle? 16 square units This reflection helps us see that the triangle is exactly half of the whole rectangle. Half of 16 is 8. This reflection helps us see that the triangle is exactly half of the whole rectangle. Half of 16 is 8. 16 square units Now, here is the rectangle that contains our triangle. What is the area of the whole rectangle?

Area of the Rectangle: 24 square units Finding the Area of Triangles Area of the Rectangle: 24 square units Here is a new triangle. This is the rectangle that contains the triangle. What is the area of the rectangle? 3 x 8 = 24, so the area of the rectangle is 24 square units. What is the area of the triangle? Let’s decompose it to find out. What is the area? This is the rectangle that contains the triangle. What is the area of the rectangle? What is the area? What is the area of the triangle? Let’s decompose it to find out. Here is a new triangle. 3 x 8 = 24, so the area of the rectangle is 24 square units.

Finding the Area of Triangles Area of the Rectangle: 24 square units Area of the Triangle: 12 square units The area of the triangle is 12 square units. It’s half the area of the rectangle. The area of the triangle is 12 square units. It’s half the area of the rectangle.

Area of the Rectangle: 36 square units Finding the Area of Triangles Area of the Rectangle: 36 square units 6 6 Let’s find the area of this triangle. It has a base of 6 units … … and a height of 6 units. What is the area of the rectangle? 6 x 6 = 36, so the area of the rectangle is 36 square units. We can see that the triangle has half the area of the rectangle. What is its area? 18 square units 6 6 x 6 = 36, so the area of the rectangle is 36 square units. 18 square units What is the area of the rectangle? Let’s find the area of this triangle. It has a base of 6 units … … and a height of 6 units. We can see that the triangle has half the area of the rectangle. What is its area?

Finding the Area of Triangles Area of the Rectangle: 36 square units 6 The area of the triangle is 18 square units. It’s half the area of the rectangle. 6 Area of the Triangle: 18 square units The area of the triangle is 18 square units. It’s half the area of the rectangle.

Finding the Area of Triangles We know that this triangle has an area of 18 square units. Now, we’ll see the triangle in a different way. We know that the base … … and the height … … can help us make a rectangle. Notice that the rectangle is broken into two smaller rectangles. This part of the triangle … … is exactly half of the smaller rectangle. And this part of the triangle … … is exactly half of the larger rectangle. The area of the triangle is 18 square units. What is the total area of the red? It is also 18 square units. … is exactly half of the larger rectangle. The area of the triangle is 18 square units. What is the total area of the red? It is also 18 square units. And this part of the triangle … … is exactly half of the smaller rectangle. We know that the base … … and the height … … can help us make a rectangle. Notice that the rectangle is broken into two smaller rectangles. This part of the triangle … We know that this triangle has an area of 18 square units. Now, we’ll see the triangle in a different way.

Finding the Area of Triangles Area of the Rectangle 8 square units What is the area of the rectangle? 8 square units 8 square units What is the area of the rectangle?

Finding the Area of Triangles Area of the Rectangle 8 square units Area of the Triangle 4 square units What is the area of the triangle? 4 square units What is the area of the triangle? 4 square units

Rectangle: 20 square units Finding the Area of Triangles Rectangle: 20 square units What is the area of the rectangle? 20 square units 20 square units What is the area of the rectangle?

Rectangle: 20 square units Triangle: 10 square units Finding the Area of Triangles Rectangle: 20 square units Triangle: 10 square units What is the area of the triangle? 10 square units 10 square units What is the area of the triangle?

Rectangle: 24 square units Finding the Area of Triangles Rectangle: 24 square units What is the area of the rectangle? 24 square units 24 square units What is the area of the rectangle?

Rectangle: 24 square units Triangle: 12 square units Finding the Area of Triangles Rectangle: 24 square units Triangle: 12 square units What is the area of the triangle? 12 square units 12 square units What is the area of the triangle?

Rectangle: 48 square units Finding the Area of Triangles Rectangle: 48 square units What is the area of the rectangle? 48 square units 48 square units What is the area of the rectangle?

Rectangle: 48 square units Triangle: 24 square units Finding the Area of Triangles Rectangle: 48 square units Triangle: 24 square units What is the area of the triangle? 24 square units 24 square units What is the area of the triangle?

Rectangle: 28 square units Finding the Area of Triangles Rectangle: 28 square units What is the area of the rectangle? 28 square units 28 square units What is the area of the rectangle?

Rectangle: 28 square units Triangle: 14 square units Finding the Area of Triangles Rectangle: 28 square units Triangle: 14 square units What is the area of the triangle? 14 square units 14 square units What is the area of the triangle?

Finding the Area of Triangles Area of the Rectangle 24 square feet 6 feet Area of the Triangle 12 square feet This shape measures 4 feet … … by 6 feet. What is the area of the rectangle? 24 square feet What is the area of the triangle? 12 square feet 4 feet 12 square feet What is the area of the triangle? This shape measures 4 feet … … by 6 feet. What is the area of the rectangle? 24 square feet

Finding the Area of Triangles Area of the Rectangle 80 square cm 8 cm Area of the Triangle 40 square cm This shape measures 10 cm … … by 8 cm. What is the area of the rectangle? 80 square cm What is the area of the triangle? 40 square cm 10 cm 40 square cm What is the area of the triangle? This shape measures 10 cm … … by 8 cm. What is the area of the rectangle? 80 square cm

What is the area of the triangle? Finding the Area of Triangles What is the area of the triangle? A = bh 2 A = 24•9 2 A = 216 2 9 km What is the area of the triangle? Let’s multiply the base times the height. What is 24 x 9? 216 The area of a triangle is ½ the base x the height. To find half of 216, let’s divide it by 2. What is 216 ÷ 2? 108 So, the area of the triangle is 108 square km. 24 24 km × 9 108 108 square km 2 216 216 What is the area of the triangle? Let’s multiply the base times the height. What is 24 x 9? 216 The area of a triangle is ½ the base x the height. To find half of 216, let’s divide it by 2. What is 216 ÷ 2? 108 So, the area of the triangle is 108 square km.

What is the area of the triangle? Finding the Area of Triangles What is the area of the triangle? 14 A = bh 2 × 22 154 308 2 308 A = 14•22 2 A = 308 2 22 miles What is the area of the triangle? Let’s multiply the base times the height. What is 14 x 22? 308 The area of a triangle is ½ the base x the height. To find half of 308, let’s divide it by 2. What is 308 ÷ 2? 154 So, the area of the triangle is 154 square miles. 14 miles 154 square miles Let’s multiply the base times the height. What is 14 x 22? What is the area of the triangle? 308 The area of a triangle is ½ the base x the height. To find half of 308, let’s divide it by 2. What is 308 ÷ 2? 154 So, the area of the triangle is 154 square miles.

What is the area of the triangle? Finding the Area of Triangles What is the area of the triangle? A = bh 2 A = 10•9 2 A = 90 2 9 cm What is the area of the triangle? Let’s multiply the base times the height. What is 10 x 9? 90 The area of a triangle is ½ the base x the height. To find half of 90, let’s divide it by 2. What is 90 ÷ 2? 45 So, the area of the triangle is 45 square cm. 10 10 cm × 9 45 45 square cm 90 2 90 Let’s multiply the base times the height. What is 10 x 9? What is the area of the triangle? 90 The area of a triangle is ½ the base x the height. To find half of 90, let’s divide it by 2. What is 90 ÷ 2? 45 So, the area of the triangle is 45 square cm.

What is the area of the triangle? Finding the Area of Triangles What is the area of the triangle? A = bh 2 A = 10•9 2 14 m A = 90 2 What is the area of the triangle? Let’s multiply the base times the height. What is 25 x 14? 350 The area of a triangle is ½ the base x the height. To find half of 350, let’s divide it by 2. What is 350 ÷ 2? 175 So, the area of the triangle is 175 square m. 25 m 25 × 14 175 350 2 350 175 square m Let’s multiply the base times the height. What is 25 x 14? What is the area of the triangle? 350 The area of a triangle is ½ the base x the height. To find half of 350, let’s divide it by 2. What is 350 ÷ 2? 175 So, the area of the triangle is 175 square m.

Finding the Area of Triangles Level 2

A = bh 2 50 = 10•h 2 50 = 5h 5 5 10 cm Finding the Area of Triangles The area of a triangle is 50 square centimeters and the base is 10 centimeters. What is the height of the triangle? A = bh 2 10 cm 50 = 10•h 2 50 = 5h 10 cm 5 5 10 cm

Finding the Area of Triangles The area of a triangle is 22 square inches and the height is 4 inches. What is the base of the triangle? A = bh 2 4 inches 22 = b•4 2 22 = 2b 11 inches 2 2 11 inches

A = bh 2 18 = 4•h 2 18 = 2h 2 2 9 meters Finding the Area of Triangles The area of a triangle is 18 square meters and the base is 4 meters. What is the height of the triangle? A = bh 2 18 = 4•h 2 9 m 18 = 2h 2 2 9 meters 4 m

A = bh 2 28 = 8•h 2 28 = 4h 4 4 7 cm Finding the Area of Triangles The area of a triangle is 28 square centimeters and the base is 8 centimeters. What is the height of the triangle? A = bh 2 7 cm 28 = 8•h 2 28 = 4h 8 cm 4 4 7 cm

Finding the Area of Triangles Lightning Round

A = bh A = bh A = 12•8 2 A = 96ft2 A = 12•4 2 A = 48h A = 96 + 24 2 Finding the Area of Triangles A = bh A = bh 2 A = 12•8 A = 96ft2 A = 12•4 2 A = 48h A = 96 + 24 2 A = 120 ft2 A = 24 ft2

A = bh A = bh A = 12•12 2 A = 144ft2 A = 8•12 2 A = 96h A = 144 + 48 2 Finding the Area of Triangles A = bh A = bh 2 A = 12•12 A = 144ft2 A = 8•12 2 A = 96h A = 144 + 48 2 A = 192 ft2 A = 48 ft2

I can… Determine the area of triangles Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Area of a Triangle 10.2 Notes Area = base • height 2 A = bh   Copy the equation (don’t just solve in your head) Substitute the numbers for the variables Solve base