Area of Parallelograms
What is the formula for the area of a parallelogram?
A=b×h
What is the formula for the area of a triangle?
A=1/2 base x height or A=base x height divided by 2
Look at Question 4 on your worksheet. What is the area of the figure?
10×7= 70 m²
What does it mean to decompose a shape?
To break a shape into smaller shapes to help find its area.
A rectangular classroom rug is 8 ft long and 6 ft wide. What is its area?
48 ft²
A parallelogram has a base of 8 cm and a height of 5 cm. What is its area?
40 cm²
A triangle has a base of 10 cm and a height of 6 cm. What is its area?
30 cm²
Look at Question 5. Decompose the L-shaped figure into two rectangles. What is the total area?
Top rectangle: 8×8=648\times8=64 cm²
Bottom rectangle: 2×4=82\times4=8 cm². So the correct answer is 72 cm².
What does it mean to compose a shape?
To put two or more shapes together to create a new shape.
A triangular flag has a base of 12 in and a height of 8 in. What is its area?
48 in²
A parallelogram has a base of 12 m, a height of 7 m, and a slanted side of 9 m. What is its area?
84 m². The 9 m is not needed.
A triangle has a base of 16 ft, a perpendicular height of 7 ft, and a slanted side of 10 ft. What is its area?
56 ft². The 10 ft is not needed.
Look at the first Question 6, the irregular gray figure. Decompose the figure into a rectangle and a triangle. What is its total area?
Rectangle: 7×7=497\times7=49 m²
Triangle: 12(5)(7)=17.5\frac12(5)(7)=17.5 m²
Total = 66.5 m²
What does parallel mean?
Lines that stay the same distance apart and never intersect.
A parallelogram-shaped garden has a base of 15 ft and a height of 8 ft. Each square foot holds 2 flowers. How many flowers can be planted?
Area = 120 ft² → 240 flowers
A parallelogram has an area of 96 ft² and a base of 12 ft. What is its height?
8 ft
A triangle has an area of 54 m² and a base of 12 m. What is its height?
9 m
Look at the second Question 6. Rectangle B measures 3 cm by 4 cm. What is the area of Rectangle B?
3×4= 12 cm²
What does perpendicular mean?
Lines that intersect to form a 90° (right) angle.
A triangular mural has a base of 18 ft and a height of 12 ft. One can of paint covers 18 ft². How many cans are needed?
Area = 108 ft²; 108 ÷ 18 = 6 cans
Two parallelograms both have a base of 14 cm. Shape A has a height of 8 cm. Shape B has a height of 11 cm. How much greater is the area of Shape B?
A = 112 cm², B = 154 cm² → 42 cm² greater
Triangle A has a base of 18 cm and height of 10 cm. Triangle B has a base of 15 cm and height of 14 cm. Which triangle has the greater area, and by how much?
A = 90 cm²; B = 105 cm² → Triangle B by 15 cm²
Second Question #6, Figures A–C
Question: Look at the second Question 6. Find the area of A, B, and C, then determine the total white area remaining after B and C are removed from A.
A: 16×14=22416\times14=224 cm²
B: 3×4=123\times4=12 cm²
C: 2×12=242\times12=24 cm²
Gray area: 12+24=3612+24=36 cm²
White area: 224−36=188 cm2
You decompose a polygon into a rectangle and a triangle. The rectangle has two opposite sides that never meet. The triangle's height meets its base at a 90° angle. What TWO vocabulary words describe these relationships?
Parallel describes the opposite sides, and perpendicular describes the height and base.
A playground has a rectangular section measuring 20 ft × 12 ft and an attached triangular section with a base of 12 ft and height of 10 ft. Rubber flooring costs $4 per square foot. How much will it cost to cover the entire playground?
Rectangle = 240 ft²; Triangle = 60 ft²; Total = 300 ft²; 300 × $4 = $1,200.