Question

what is the total surface area of the figure

32 m 20 m 12 m 10 m 8 m

Answer 1

To find the total surface area of the figure, we need to calculate the area of each face and then add them up.

Given:
- Length = 32 m
- Width = 20 m
- Height (or Depth) = 12 m
- Side of the square base = 10 m
- Slant height of the pyramid = 8 m

Area of the front face (rectangle):
= length * height
= 32 * 12
= 384 m^2

Area of the back face (rectangle):
= length * height
= 32 * 12
= 384 m^2

Area of the left face (square):
= side^2
= 10^2
= 100 m^2

Area of the right face (square):
= side^2
= 10^2
= 100 m^2

Area of the bottom face (rectangle):
= length * width
= 32 * 20
= 640 m^2

Area of the front triangular face of the pyramid:
= 0.5 * base * height
= 0.5 * 10 * 8
= 40 m^2

Area of the back triangular face of the pyramid:
= 0.5 * base * height
= 0.5 * 10 * 8
= 40 m^2

Now, let's add up all the areas to find the total surface area:
384 + 384 + 100 + 100 + 640 + 40 + 40 = 1688

Therefore, the total surface area of the figure is 1688 square meters.