Question

NO LINKS!! Find the areas of these composite figures​

Answer 1

a) 92.5 in² (nearest tenth)

b) 260 m²

Explanation:

Formulas

`\textsf{Area of a rectangle}=\textsf{width} * \textsf{length}`

`\textsf{Area of a triangle}=\frac12 * \sf base * height`

`\textsf{Area of a semicircle}=\frac12 \pi r^2 \quad \textsf{(where r is the radius)}`

`\textsf{Radius of a circle}=(1)/(2)d \quad \textsf{(where d is the diameter)}`

Part (a)

This figure comprises:

• an isosceles triangle (with base of 12 in and height of 6 in)
• a semicircle (with radius of 6 in)

Total Area:

= area of triangle + area of semicircle

`\sf = (1)/(2) \cdot 12 \cdot 6+(1)/(2) \pi (6)^2`

`\sf = 36 + 18 \pi`

`\sf = 92.5 \:\: in^2 \:(nearest\:tenth)`

Part (b)

This figure comprises:

• an isosceles triangle (with base of 10 m and height of 12 m)
• a rectangle (with width of 10 m and length of 20 m)

Total Area:

= area of triangle + area of rectangle

`\sf = (1)/(2) \cdot 10 \cdot 12+10 \cdot 20`

`\sf = 60+200`

`\sf = 260 \:\: m^2`

Answer 2

A) Area of triangle = 1/2 x 6 x 12 = 36

Area of semi circle = 1/2 x PI x 6^2 = 56.52

Total area = 36 + 56.52 = 92.52 square inches

B) Area of triangle = 1/2 x 10 x 12 = 60

Area of rectangle = 20 x 10 = 200

Total area = 200 + 60 = 260 square inches