surface area and volume

[Amanda[Miss Math]]

A square pyramid has a base with a perimeter of 24 inches and a height of 4 inches. Find the surface area and volume of the pyramid.

I alredy know that SA= LA+B
and V= 1/3BH
But I'm sooo confused, please help!!!

 

[galactus]

Since it is square and the base has area 24, then it must have side lengths of 6.

Therefore, the area of the base is 6^2=36.

Now, we can find the volume.

As for the surface area, we already know the area of the base. Now, to find the area of the 4 sides.

The slant height of the sides can be gotten from Pythagoras. \(\displaystyle \sqrt{4^{2}+3^{2}}=5\)

Now, there are 4 equilateral triangles that make up the sides to find the area of. Find the area of the triangles and add the base area to have the total surface area.

 

[Denis]

GO GO Miss Math: you can do it ! :idea: