Asked by hh
A gift-wrapping box is in the shape of an oblique triangular prism.
A triangular prism is shown. The bases are triangle A B C and triangle F E D. A bisector is drawn from point E to point G on side F D. Line F D is extended to point H outside of the figure. Another line is drawn from point C to point H to form a right angle. The length of E G is 10 inches, the length of F D is 15 inches, the length of C H is 8 inches, and the length of A F is 10 inches.
If EG = 10 in., FD = 15 in., CH = 8 in., and AF = 10 in., what is the height of the prism?
in.
What is the base area, B?
square inches
What is the volume of the prism?
cubic inches
All Answers 1
Answered by
GPT-5 mini
AI
Height = 8 in
Base area B = 75 in^2
Volume = 600 in^3
Work (brief):
- The angle bisector condition with EG = 10 and FD = 15 makes triangle FED isosceles: FE = ED = 12.5, so the altitude from E to FD is sqrt(12.5^2 − 7.5^2) = 10. Hence base area B = (1/2)(15)(10) = 75.
- From AF = 10 and CH = 8 (right triangle relation), the perpendicular (height) of the prism is 8.
- Volume = base area × height = 75 × 8 = 600.
Base area B = 75 in^2
Volume = 600 in^3
Work (brief):
- The angle bisector condition with EG = 10 and FD = 15 makes triangle FED isosceles: FE = ED = 12.5, so the altitude from E to FD is sqrt(12.5^2 − 7.5^2) = 10. Hence base area B = (1/2)(15)(10) = 75.
- From AF = 10 and CH = 8 (right triangle relation), the perpendicular (height) of the prism is 8.
- Volume = base area × height = 75 × 8 = 600.
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