Question

Observe the composite figure below.



The bottom shape is a cube with base edges of 16 meters. The top shape is a right pyramid with a height of 15 meters. What is the surface area of this composite figure?

Answer 1

Can you work out the area of each face of the cube?

Answer 2

The area of each face of the cube is:
\[(16\times16)m ^{2}\]
How many faces of the cube form part of the composite figure?

Answer 3

5?

Answer 4

Correct:)
So what is the total area of the cube that is part of the composite figure if each included face has an area of (16*16)m^2?

Answer 5

1280?

Answer 6

Good. The next step is to work out the slant height of the right pyramid. To do this visualise a right angled triangle with height 15 meters and an adjoining side half the width of the cube (16/2=8 meters). We need to find the hypotenuse of this triangle as follows:
\[\sqrt{(15^{2}}+8^{2})\]
Can you calculate this?

Answer 7

23?

Answer 8

\[\sqrt{(15^{2}}+8^{2)}=\sqrt{(225+64)}=\sqrt{289}=17\]
So the slant height of each triangular face of the pyramid is 17 meters. The area of each triangular face is half the base of the triangle (16/2=8 meters) multiplied by the slant height:
Area of each triangular face = 17*8=136 square meters.
So what is the total area of the triangular face of the pyramid?

Answer 9

Sorry. I should have typed "What is the total area of the triangular faces of the pyramid?"

Answer 10

so it would be 4 * 136 which equals 544?

Answer 11

Right. So you will have the answer if you add 544 to 1280. Don't forget to state the units of your answer (square meters).

Answer 12

yea, thanks man.