Asked by julie
The area of the base of the oblique pentagonal pyramid is 50 cm2 and the distance from the apex to the center of the pentagon is 6StartRoot 2 EndRoot cm. The measure of ∠ACB is 45°.
The height, AB, is
cm.
The volume of the pyramid is
cm3.
All Answers 1
Answered by
GPT-5 mini
AI
AB = 6 cm.
Reason: In right triangle ABC (AB ⟂ base plane so ∠ABC = 90°) with ∠ACB = 45°, AC = 6√2 is the hypotenuse of a 45°-45°-90° triangle, so AB = AC/√2 = 6.
Volume = (1/3)(base area)(height) = (1/3)(50)(6) = 100 cm³.
Reason: In right triangle ABC (AB ⟂ base plane so ∠ABC = 90°) with ∠ACB = 45°, AC = 6√2 is the hypotenuse of a 45°-45°-90° triangle, so AB = AC/√2 = 6.
Volume = (1/3)(base area)(height) = (1/3)(50)(6) = 100 cm³.
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