Step by step
The question
Question: find the surface area of a rectangular pyramid with base 14 by 20, and slant heights 26 and 25.
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, 14 by 20.
Its area is length times width: 14 × 20.
14 times 20 is 280.
So the base is 280 square units.
3 Front and back
The front triangle has base 14.
Its height is the slant height up its middle: 26.
One triangle is half of base times height: ½ × 14 × 26.
14 times 26 is 364.
Half of 364 means 364 divided by 2.
That is 182.
So the front is 182 square units.
The back is the same.
2 times 182 is 364.
4 Left and right
The side triangle is different.
Its base is 20, and its slant height is 25.
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 × 25.
20 times 25 is 500.
Half of 500 means 500 divided by 2.
That is 250.
So one side is 250 square units.
The other side is the same.
2 times 250 is 500.
5 Add all the faces
Add the base and the two pairs: 280 + 364 + 500.
280 plus 364 plus 500 is 1144.
So the surface area is 1144 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.