Step by step
The question
Question: find the surface area of a rectangular pyramid with base 9.6 by 3, and slant heights 2.5 and 5.2.
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, 9.6 by 3.
Its area is length times width: 9.6 × 3.
Forget the points: 96 times 3 is 288.
The numbers have 1 digit after the point.
So the answer has 1 too: 28.8.
So the base is 28.8 square units.
3 Front and back
The front triangle has base 9.6.
Its height is the slant height up its middle: 2.5.
One triangle is half of base times height: ½ × 9.6 × 2.5.
Forget the points: 96 times 25 is 2400.
Together, the numbers have 1 + 1 = 2 digits after the point.
So the answer has 2 too: 24.00, which is 24.
Half of 24 means 24 divided by 2.
That is 12.
So the front is 12 square units.
The back is the same.
2 times 12 is 24.
4 Left and right
The side triangle is different.
Its base is 3, and its slant height is 5.2.
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 × 3 × 5.2.
Forget the points: 3 times 52 is 156.
The numbers have 1 digit after the point.
So the answer has 1 too: 15.6.
Half of 15.6 means 15.6 divided by 2.
That is 7.8.
So one side is 7.8 square units.
The other side is the same.
2 times 7.8 is 15.6.
5 Add all the faces
Add the base and the two pairs: 28.8 + 24 + 15.6.
28.8 plus 24 plus 15.6 is 68.4.
So the surface area is 68.4 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.