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

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=c²apply 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

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