Step by step
The question
Question: find the surface area of a rectangular pyramid with base 36 by 14, and slant heights 25 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 14.
Its area is length times width: 36 × 14.
36 times 14 is 504.
So the base is 504 square units.
3 Front and back
The front triangle has base 36.
Its height is the slant height up its middle: 25.
One triangle is half of base times height: ½ × 36 × 25.
36 times 25 is 900.
Half of 900 means 900 divided by 2.
That is 450.
So the front is 450 square units.
The back is the same.
2 times 450 is 900.
4 Left and right
The side triangle is different.
Its base is 14, 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 × 14 × 30.
14 times 30 is 420.
Half of 420 means 420 divided by 2.
That is 210.
So one side is 210 square units.
The other side is the same.
2 times 210 is 420.
5 Add all the faces
Add the base and the two pairs: 504 + 900 + 420.
504 plus 900 plus 420 is 1824.
So the surface area is 1824 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.