Composite Figures

Composite Figures

Composite figures are figures that are made from more than one shape being combined. The heart that you see is actually made from a square and two semi-circles.

To calculate composite figures' area, you need to be able to find the area of simple shapes first.

LET'S PRACTICE!

For rectangles, you multiply the length x width.

You may also hear that area of a rectangle is calculated using the formula Area= base x height.

Multiple Choice

4. What is the area of the rectangle?

• 30 mm²

• 36 mm²

• 45 mm²

• 56 mm²

Multiple Choice

5. What is the area of the rectangle?

• 8 ft²

• 9 ft²

• 10 ft²

• 12 ft²

Area of a square is similar to area of a rectangle. You multiply length x width.

To find area of this square, I'd multiply 5 x 5

Multiple Choice

7. Find the area of this square.

• 25 cm

• 20 cm²

• 25 cm²

• 55 cm

Multiple Choice

8. What is the formula for the area of a rectangle?

• Length x Width

• Length x Length

• Width x Width

Multiple Choice

9. What is the formula for the area of a square?

• Length x Width

• Length x Length

• Width x Width

For area of a triangle, you multiply base x height. Then, divide your answer by 2.

These triangles look different, but the height is determined by the perpendicular line that makes a right angle.

The triangle has a base of 6 and a height of 7.

To solve, first multiply base x height.

7 x 6 = 42 Then, divide by 2. 42/2 = 21 Area = 21 cm^2

Multiple Choice

12. How do you find the area of a triangle?

• base x height

• take half of the base times the height

• add up all of the sides

Multiple Choice

13. Find the area of this triangle.

• 20 cm²

• 35 cm²

• 40 cm²

• 17.5 cm²

Multiple Choice

14. What is the area of a triangle with a base of 10 cm and a height of 14 cm?

• 24 cm squared

• 12 cm squared

• 70 cm squared

• 140 cm squared

Area of a trapezoid is found when you add base 1 and base 2, then divide by 2. After that, multiply times the height.

Example

• The bases are 9 and 16

• 9 + 16 = 25

• 25 / 2 = 12.5

• Take this answer x height

• 12.5 x 5 = 62.5 units squared

Multiple Choice

Find the area of this trapezoid

• 49 units squared

• 238 units squared

• 85 units squared

Parallelograms

Area equals the base times the height.

Multiple Choice

Find the area of this parallelogram.

• 50 inches

• 50 inches squared

• 60 inches squared

• 21 inches squared

Area of a circle is $\pi r^2$  

What would be the formula for a semicircle??

Composite Area is the area of the combined shapes. To find composite area, you must:

1) Break the figure into smaller shapes.

2) Write the formula for area of each shape.

3) Calculate the area of each shape

4) Add all of the areas

Open Ended

What kind of shapes make up this composite shape?

Multiple Choice

16. What is the area of the composite figure?

• 48 cm²

• 90 cm²

• 78 cm²

• 12 cm²

Multiple Choice

18. The arrow shown is on a sign. What is the area of the arrow?

• 17 in²

• 40 in²

• 52 in²

• 61 in²

Multiple Choice

17. What is the area of the shaded region?

• 14 m²

• 120 m²

• 106 m²

• 134 m²