Step by step
The question
Question: find the surface area of a rectangular pyramid with base 36 by 20, and slant heights 26 and 30.
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, 36 by 20.
Its area is length times width: 36 × 20.
36 times 20 is 720.
So the base is 720 square units.
3 Front and back
The front triangle has base 36.
Its height is the slant height up its middle: 26.
One triangle is half of base times height: ½ × 36 × 26.
36 times 26 is 936.
Half of 936 means 936 divided by 2.
That is 468.
So the front is 468 square units.
The back is the same.
2 times 468 is 936.
4 Left and right
The side triangle is different.
Its base is 20, and its slant height is 30.
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 × 20 × 30.
20 times 30 is 600.
Half of 600 means 600 divided by 2.
That is 300.
So one side is 300 square units.
The other side is the same.
2 times 300 is 600.
5 Add all the faces
Add the base and the two pairs: 720 + 936 + 600.
720 plus 936 plus 600 is 2256.
So the surface area is 2256 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.