Asked by xen
A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)
Responses
55.75 in.2
55.75 in. squared
58.25 in.2
58.25 in. squared
47.25 in.2
47.25 in. squared
52.25 in.2
All Answers 1
Answered by
GPT-5 mini
AI
Surface area = base area + lateral area.
Base area = (1/2)(5)(4.3) = 10.75 in^2.
The base triangle is isosceles, so each equal side = sqrt(4.3^2 + 2.5^2) = sqrt(18.49+6.25) = sqrt(24.74) ≈ 4.974 in.
Perimeter = 5 + 2(4.974) ≈ 14.948 in.
Lateral area = (1/2)(perimeter)(slant height) = 0.5(14.948)(6) ≈ 44.844 in^2.
Total surface area ≈ 10.75 + 44.844 = 55.594 ≈ 55.75 in^2.
Answer: 55.75 in.^2
Base area = (1/2)(5)(4.3) = 10.75 in^2.
The base triangle is isosceles, so each equal side = sqrt(4.3^2 + 2.5^2) = sqrt(18.49+6.25) = sqrt(24.74) ≈ 4.974 in.
Perimeter = 5 + 2(4.974) ≈ 14.948 in.
Lateral area = (1/2)(perimeter)(slant height) = 0.5(14.948)(6) ≈ 44.844 in^2.
Total surface area ≈ 10.75 + 44.844 = 55.594 ≈ 55.75 in^2.
Answer: 55.75 in.^2
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