WAY back when… You found areas of rectangles and squares. Find perimeters and areas of parallelograms. Find perimeters and areas of triangles. Now we will.

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Presentation transcript:

WAY back when… You found areas of rectangles and squares. Find perimeters and areas of parallelograms. Find perimeters and areas of triangles. Now we will

Vocabulary base of a parallelogram height of a parallelogram base of a triangle height of a triangle

How do we find area of a PARALLELOGRAM? What shapes does this include? Squares! Rectangles! Rhombi!

Ex: 1 Find the perimeter and area of Perimeter: Opposite Sides of a parallelogram are congruent! 20in + 32in + 20in + 32in = 104in Area = b*h b=32 h= Let’s find h! 16

You Try! A.88 m; 255 m 2 B.88 m; 405 m 2 C.88 m; 459 m 2 D.96 m; 459 m 2 Find the perimeter and area of

Ex: 2 Find the area of Area = b*h b=12 h= Let’s find h! Using Triangles:

Ex: 3 Find the height and base of the parallelogram if the area is 168 square units. A side length cannot be negative, so x=12! Plugging x=12 in for x+2, our other side length is 14! =12 14

Your Turn! A.156 cm 2 B cm 2 C.192 cm 2 D cm 2 Find the area of

How do we find the area of a TRIANGLE?

EX: 4 Real world: You need to buy enough wooden boards to make the frame of the triangular sandbox shown and enough sand to fill it. If one board is 3 feet long and one bag of sand fills 9 square feet of the sandbox, how many boards and bags do you need to buy? First: Find area of sandbox to estimate how many bags of sand are needed. Second, Find the perimeter of the sandbox to estimate how many boards are needed.

Ex: 4 continuted.. Boards: Each board is 3 feet Bags of Sand: Each bag fills 9ft² of area boards Third, Use P=35.5ft and A=54ft² to determine how many boards and bags of sand will be needed! You would need 12 boards, and 6 bags of sand!

Ex: 5 Find the area of the equilateral triangle: 9in 60° 15.6in

Changing Dimensions What happens to the perimeter if we take a triangle and triple its size? P=12 P=36 The perimeter also Triples!

What happens to the area if we triple its size?

Concept:

Next slide can be used for composites.

Ex: 6 When viewed from above, the base of a water fountain has the shape of a hexagon, composed of a square and 2 congruent isosceles right triangles. What is the perimeter and area of the following layout for the fountain? First, find the area of the square. 20ft Second, find the area of one triangle. 20ft Total Area: 400ft²+200ft² Total Area: 600ft²

Continued… 20ft Now, find the perimeter of the figure. 20ft Side lengths of the square: 20ft each Side lengths of the triangles? 45° Use triangles!