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The perimeter of the base of square pyramid is 40 centimetres and the total length of all its edges is 92 centimetres. Calculate its surface area. |
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Answer» Base perimeter = 4a = 40 a = 10cm Total length of edges = 92 cm Length of total laterals edge = 92 – 40 = 52 Length of one laterals edge = \(\frac{52}{4}\) = 13 cm Slant height of lateral surfaces is l = \(\sqrt{13^{12} - 5^2}\) = \(\sqrt{169-25}\) = \(\sqrt{144}\) = 12 cm Surface area of pyramid = Base area + 2 x Perimeter of base x length of slant height of lateral surfaces = a2 + 1/2 pl = 102 + 1/2 x 40 x 12 = 100 + 240 = 340 cm2 OR Surface area of pyramid = a2 + 2 al = 102 + 2 × 10 × 12 = 100 + 240 = 340 cm2 |
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