Step by step
The question
Question: find the surface area of a rectangular pyramid with base 6 by 15, and slant heights 8.5 and 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, 6 by 15.
Its area is length times width: 6 × 15.
6 times 15 is 90.
So the base is 90 square units.
3 Front and back
The front triangle has base 6.
Its height is the slant height up its middle: 8.5.
One triangle is half of base times height: ½ × 6 × 8.5.
Forget the points: 6 times 85 is 510.
The numbers have 1 digit after the point.
So the answer has 1 too: 51.0, which is 51.
Half of 51 means 51 divided by 2.
That is 25.5.
So the front is 25.5 square units.
The back is the same.
2 times 25.5 is 51.
4 Left and right
The side triangle is different.
Its base is 15, and its slant height is 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 × 15 × 5.
15 times 5 is 75.
Half of 75 means 75 divided by 2.
That is 37.5.
So one side is 37.5 square units.
The other side is the same.
2 times 37.5 is 75.
5 Add all the faces
Add the base and the two pairs: 90 + 51 + 75.
90 plus 51 plus 75 is 216.
So the surface area is 216 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.