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
