Question

What is the surface area of the object shown below?

Answer 1

See a solution process below:

Explanation:

The object is made up of the following shapes which have the areas:

T1: Top is a rectangle 10 ft xx 36ft = `360"ft"^2`

R2: Left Side is a rectangle 10 ft xx 20ft = `200"ft"^2`

R3: Right Side is a rectangle 10 ft xx 25ft = `250"ft"^2`

B: Bottom is a rectangle 10 ft xx (36ft + 15ft) = 10 ft xx 51 ft = `510"ft"^2`

R1: Front and Back Rectangles are both rectangles of the same size of 36 ft xx 20 ft = `720"ft"^2`

Because there is a front and back we need to multiply this by 2:

`720"ft"^2 xx 2 = 1440"ft"^2`

T2: Front and Back Triangles are both triangles of the same size of base is: 15 ft and height is: 20 ft

The formula for the area of a triangle is: `1/2bh`

Area of T2 is #1/2 xx 15"ft" xx 20 "ft" = 150"ft"^2

Because there is a front and back we need to multiply this by 2:

`150"ft"^2 xx 2 = 300"ft"^2`

Therefore, the entire surface area of the object in the pictures is:

`S = T_1 + R_2 + R_3 + B + 2R_1 + 2T_2 =`

`360"ft"^2 + 200"ft"^2 + 250"ft"^2 + 510"ft"^2 + 1440"ft"^2 + 300"ft"^2 =`

`3060"ft"^2`