Step by step
The question
Question: find the surface area of a rectangular pyramid with base 20 m by 14 m, and slant heights 25 m and 26 m.
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, 20 by 14.
Its area is length times width: 20 × 14.
20 times 14 is 280.
So the base is 280 m².
3 Front and back
The front triangle has base 20 m.
Its height is the slant height up its middle: 25 m.
One 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 the front is 250 m².
The back is the same.
2 times 250 is 500.
4 Left and right
The side triangle is different.
Its base is 14 m, and its slant height is 26 m.
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 × 14 × 26.
14 times 26 is 364.
Half of 364 means 364 divided by 2.
That is 182.
So one side is 182 m².
The other side is the same.
2 times 182 is 364.
5 Add all the faces
Add the base and the two pairs: 280 + 500 + 364.
280 plus 500 plus 364 is 1144.
So the surface area is 1144 m².
Let's look back.
First: count the faces.
Then: the base.
Then: front and back.
Then: left and right.
Last: add all the faces.