9514 1404 393
Answer:
B = 6.65 in²
Step-by-step explanation:
The base area (B) is the area of the triangular base of the prism. You already know the sides of that triangle are 3, 5, and 7 inches. The figure shows the altitude to the side length 7 is 1.9 inches. The triangle area formula applies:
A = 1/2bh
A = 1/2(7 in)(1.9 in) = 6.65 in² . . . . area of one triangular base.
Then the area of one base is B = 6.65 in².
__
The lateral area is the product of the perimeter and the height:
LA = Ph = 15(12) = 180 . . . . square inches
The total surface area is the sum of the lateral area and the areas of the two bases.
SA = LA + 2B
SA = 180 in² + 2(6.65 in²) = 193.3 in²
