Step by step
The question
Question: find the surface area of a rectangular pyramid with base 14.4 by 8, and slant heights 5 and 7.8.
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, 14.4 by 8.
Its area is length times width: 14.4 × 8.
Forget the points: 144 times 8 is 1152.
The numbers have 1 digit after the point.
So the answer has 1 too: 115.2.
So the base is 115.2 square units.
3 Front and back
The front triangle has base 14.4.
Its height is the slant height up its middle: 5.
One triangle is half of base times height: ½ × 14.4 × 5.
Forget the points: 144 times 5 is 720.
The numbers have 1 digit after the point.
So the answer has 1 too: 72.0, which is 72.
Half of 72 means 72 divided by 2.
That is 36.
So the front is 36 square units.
The back is the same.
2 times 36 is 72.
4 Left and right
The side triangle is different.
Its base is 8, and its slant height is 7.8.
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 × 8 × 7.8.
Forget the points: 8 times 78 is 624.
The numbers have 1 digit after the point.
So the answer has 1 too: 62.4.
Half of 62.4 means 62.4 divided by 2.
That is 31.2.
So one side is 31.2 square units.
The other side is the same.
2 times 31.2 is 62.4.
5 Add all the faces
Add the base and the two pairs: 115.2 + 72 + 62.4.
115.2 plus 72 plus 62.4 is 249.6.
So the surface area is 249.6 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.