Question

Find the lateral area and the volume of the regular pyramid

Answer 1

Lateral Area: 1/2 * perimeter of base * slant height

Surface area: Lateral area + area of base


1/2 * 12 * 4
Surface area = 24 units squared

24 + ( 1/2 * 4 * 4 )
Surface area = 32 units squared

Answer 2

Volume = 1/3 * base area * height

1/3 * 8 * height

Answer 3

I got the height to be 3.5

I found that by doing the Pythagorean theorm. Take the hypotenuse ( 4 ) and squared it ( 16 ) minus 2 squared ( 4 ) ,because you take 1/2 the length of the base to make a right triangle inside that triangle, to get 12. Then you take the square root of 12 which rounds to 3.5.

So the volume is 9.3 units cubed