Step by step
The question
Question: find the surface area of a rectangular pyramid with base 5 by 16, and slant heights 10 and 6.5.
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, 5 by 16.
Its area is length times width: 5 × 16.
5 times 16 is 80.
So the base is 80 square units.
3 Front and back
The front triangle has base 5.
Its height is the slant height up its middle: 10.
One triangle is half of base times height: ½ × 5 × 10.
5 times 10 is 50.
Half of 50 means 50 divided by 2.
That is 25.
So the front is 25 square units.
The back is the same.
2 times 25 is 50.
4 Left and right
The side triangle is different.
Its base is 16, and its slant height is 6.5.
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 × 16 × 6.5.
Forget the points: 16 times 65 is 1040.
The numbers have 1 digit after the point.
So the answer has 1 too: 104.0, which is 104.
Half of 104 means 104 divided by 2.
That is 52.
So one side is 52 square units.
The other side is the same.
2 times 52 is 104.
5 Add all the faces
Add the base and the two pairs: 80 + 50 + 104.
80 plus 50 plus 104 is 234.
So the surface area is 234 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.