Area of 2D shapes

Quadrilaterals A quadrilateral is a geometric figure that is made up of four line segments, called sides, that intersect only at their endpoints.

What are parallel lines? Two lines that never intersect.

Special Quadrilaterals Trapezoid – A quadrilateral with exactly 1 pair of parallel sides. Parallelogram – A quadrilateral with 2 pairs of parallel sides.

What is the area of this parallelogram? PARALLELOGRAM CUT HERE! S=side H=height B=base

What is the area of this parallelogram? PARALLELOGRAM MOVE TO HERE! B=base H=height

It’s the same as the area of this rectangle! PARALLELOGRAM H=height B=base

Area parallelogram = Base x Height (perpendicular height H) PARALLELOGRAM B=base Side H=height

To find the area of a parallelogram, you always multiply the base and the height. So, Area = base x height or A = bh Remember: The height is the line segment that is perpendicular to the base and creates a right angle. 12 in 10 in What is the area of this parallelogram? Area = base x height A = (10)(10) A = 100 in²

Your Turn Find the area and perimeter of the parallelogram. 12 cm 14 cm P = P = 52 cm

Area of a Triangle 1 2 Area of parallelogram = base x height Area of triangle = base x height Area = bh

Finding the Area of a Triangle 1. Write the formula for area of a triangle. 2. Substitute in values. 3. Simplify. 11 ft 23 ft A= bh 11 A= (23)(11) A= ft²

You try! Find the area and perimeter of the triangle. 17 m 13.4 m 20 m 15 m P = P = 52 m

Given the formula for the area of a parallelogram we are going to use that information to discover the formula for the area of a trapezoid. Watch carefully not to miss it!

Notice that the trapezoid is half the area of the parallelogram. (b 1 + b 2 ) h Copy the trapezoid, flip it over, and put it next to the original. It makes a parallelogram. We are going to use the area of a parallelogram to find the area of a trapezoid. It takes two trapezoids to make one parallelogram.

(b 1 + b 2 ) h Parallelogram Trapezoid Notice that the trapezoid is half the area of the parallelogram. How do we find half the area ? A = (b 1 + b 2 ) h Hint: Think of area of a triangle.

Area of Trapezoid 2 in 6 in 3 in A = (b 1 + b 2 ) h 4 in A = (2 + 6) 3 A = (8) 3 A = 4 3 A = 12 in² 4 in Perimeter of Trapezoid P = P = 16 in

Area of Trapezoid 3 m 8 m 4 m 5 m A = (b 1 + b 2 ) h A = (3 + 8) 4 A = (11) 4 A = (44) A = 22 m²

Practice!