SOLUTION: opqrs is a right pyramid whose base is a square of sides 12cm each. given that the slant height of the pyramid is 15 cm. find, a)height of the pyramid b)the volume of the pyrami

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Question 1103454: opqrs is a right pyramid whose base is a square of sides 12cm each. given that the slant height of the pyramid is 15 cm. find,
a)height of the pyramid
b)the volume of the pyramid
c)the total surface area of the pyramid
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The side of the base is 12; so the distance across the base from one side to the other is 12; so the distance from the middle of one side of the base to the center of the base is 6.

Then with a slant height of 15, the height of the pyramid is the other leg of a right triangle with hypotenuse 15 and one leg 6:
sqrt%2815%5E2-6%5E2%29+=+sqrt%28225-36%29+=+sqrt%28189%29+=+3%2Asqrt%2821%29

Answer a: 3%2Asqrt%2821%29 (cm)

The volume of the pyramid is %281%2F3%29Bh+=+%281%2F3%29%28144%29%283%2Asqrt%2821%29%29+=+144%2Asqrt%2821%29
Answer b: 144%2Asqrt%2821%29 (cubic cm)

The area of the base is 144; the area of each triangular face is %281%2F2%29bh+=+%281%2F2%29%2812%29%2815%29+=+90
The total surface area is 144%2B4%2890%29+=+144%2B360+=+504 (square cm)