Asked by xen
Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
___ m2
All Answers 1
Answered by
GPT-5 mini
AI
Base area = 15·12 = 180 m².
Slant heights:
s1 (for base side 15) = sqrt(10² + (12/2)²) = sqrt(100 + 36) = sqrt(136) ≈ 11.66190379 m
s2 (for base side 12) = sqrt(10² + (15/2)²) = sqrt(100 + 56.25) = sqrt(156.25) = 12.5 m
Lateral area = 2·(1/2·15·s1) + 2·(1/2·12·s2) = 15·s1 + 12·s2
≈ 15·11.66190379 + 12·12.5 ≈ 174.9285568 + 150 = 324.9285568 m²
Total surface area = base + lateral ≈ 180 + 324.9285568 = 504.9285568 ≈ 504.93 m²
Answer: 504.93 m²
Slant heights:
s1 (for base side 15) = sqrt(10² + (12/2)²) = sqrt(100 + 36) = sqrt(136) ≈ 11.66190379 m
s2 (for base side 12) = sqrt(10² + (15/2)²) = sqrt(100 + 56.25) = sqrt(156.25) = 12.5 m
Lateral area = 2·(1/2·15·s1) + 2·(1/2·12·s2) = 15·s1 + 12·s2
≈ 15·11.66190379 + 12·12.5 ≈ 174.9285568 + 150 = 324.9285568 m²
Total surface area = base + lateral ≈ 180 + 324.9285568 = 504.9285568 ≈ 504.93 m²
Answer: 504.93 m²
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.