To find: the lateral and surface area of the triangular pyramid.
Answer to Problem 8PPS
The surface area of the triangular pyramid is
Explanation of Solution
Given:
Base side length is 6 in.
Base area is
Slant height is 8 in.
Formula used:
The lateral area L of a triangular pyramid is given by the formula
The surface area S of a triangular pyramid is given by the formula
S = L + B
Calculation:
The objective is to find the lateral and surface area of the triangular pyramid.
First convert the mixed number into decimal.
First find the lateral area of the triangular pyramid.
The perimeter P of the triangular is
P = 3(side)
Put side = 6 in the perimeter formula to find the perimeter of the triangular Thus,
The slant height of the triangular pyramid is 8 in.
Put P = 18 and l = 8 in the lateral surface area to find the lateral surface area of the triangular pyramid.
Therefore, the lateral area of the triangular pyramid is
Next find the surface area of the triangular pyramid
The area B of the base is
Put B = 15.6 and L = 72 in the surface area formula to find the surface area of the triangular pyramid.
Conclusion:
Therefore, the surface area of the triangular pyramid is
Chapter 12 Solutions
Pre-Algebra Student Edition
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