Question

All the edges of a regular square pyramid have length 8. find the Volume of the pyramid, Lateral area of the pyramid and the Total surface area of the pyramid

Answer 1

Answer:

1.120.68 cubic units

2.128 square units

3.192 square units

Step-by-step explanation:

First find the height of the pyramid.

Apply Pythagorean relationship where the base is a square, find the hypotenuse

a²+b²=c²---------apply this on the square base to find the length of the diagonal then divide by  2 to get the length from one square base to the center of the pyramid. With this length and the slant height, you can find the height of the pyramid.

8²+8²=c²

64+64=c²

128=c²

√128=c

11.31=c

c/2= 5.7

Finding height of the pyramid

8²-5.7²=h²

64-32=h²

32=h²

√32=h

5.7=h

Finding volume of the pyramid

v=a²*h/3 where a is the length of the edges=8  and h is the height of the pyramid= 5.7

v=8²* 5.7/3

v=64*1.889 =120.68 cubic units

2.

Lateral area of the pyramid is calculated by finding the product of the slant height of the pyramid and half the perimeter of the base.

L.S.A=1/2p*l where p is perimeter of the base and l is the slant height

slant height =8

Perimeter of the base= 8*4 =32

Half the perimeter of the base= 32/2=16

Lateral area= 16*8=128 square units

3. The total surface area of the pyramid is given by;

T.S.A=1/2p*l +B where B is area of the base

Area of the base=8*8=64

Lateral area= 128

T.S.A= 128+64 =192 square units