9514 1404 393
Answer:
B. 75.8 ft²
Step-by-step explanation:
The height of each triangle can be found using the Pythagorean theorem. The given edge length (7 ft) is the hypotenuse of the triangle, and the base edge length is twice one leg of the triangle.
The height of the triangle on the 2 ft faces is ...
√(7² -1²) = √48 = 4√3
The height of the triangle on the 8 ft faces is ...
√(7² -4²) = √33
The areas of the triangular faces are the product of the height and half the base length:
A = 1/2bh
2 ft edge triangle area = (1/2)(2 ft)(4√3 ft) = 4√3 ft²
8 ft edge triangle area = (1/2)(8 ft)(√33 ft) = 4√33 ft²
__
The area of the rectangular base is ...
A = LW
A = (8 ft)(2 ft) = 16 ft²
__
The total surface area of the pyramid is the sum of the areas of the triangular faces and the area of the rectangular base.
2(4√3 +4√33) +16 = 8(2+√3+√33) ≈ 75.813
The total surface area is about 75.8 ft².
