Step by step
The question
Question: find the surface area of a rectangular pyramid with base 32 by 10, and slant heights 13 and 20.
1 Count the faces
The surface area is the area of all the outside faces.
This pyramid has a rectangle base and 4 triangles.
The front and back are the same.
The left and right are the same.
2 The base
The base is a rectangle, 32 by 10.
Its area is length times width: 32 × 10.
32 times 10 is 320.
So the base is 320 square units.
3 Front and back
The front triangle has base 32.
Its height is the slant height up its middle: 13.
One triangle is half of base times height: ½ × 32 × 13.
32 times 13 is 416.
Half of 416 means 416 divided by 2.
That is 208.
So the front is 208 square units.
The back is the same.
2 times 208 is 416.
4 Left and right
The side triangle is different.
Its base is 10, and its slant height is 20.
Careful!
The side triangles are not the same as the front and back.
They have their own base and slant height.
One side triangle is half of base times height: ½ × 10 × 20.
10 times 20 is 200.
Half of 200 means 200 divided by 2.
That is 100.
So one side is 100 square units.
The other side is the same.
2 times 100 is 200.
5 Add all the faces
Add the base and the two pairs: 320 + 416 + 200.
320 plus 416 plus 200 is 936.
So the surface area is 936 square units.
Let's look back.
First: count the faces.
Then: the base.
Then: front and back.
Then: left and right.
Last: add all the faces.