You use the glass pyramid shown to display rainbows on the walls of a room. The pyramid is regular and has a surface area of 105.35 square centimeters. Find the height of each triangular face. Justify your answer.

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Solution

Surface area of pyramid = Area of base + area of lateral surfaces
$105.35 c m^{2} = (\frac{1}{2} \times 7 \times 6.1 + 3 \times \frac{1}{2} \times 7 \times h) c m^{2}$
$105.35 - 21.35 = 3 \times \frac{1}{2} \times 7 \times h 84 = 3 \times \frac{1}{2} \times 7 \times h h = 8 c m$
Final answer: The height of pyramid is $8 c m$

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You use the glass pyramid shown to display rainbows on the walls of a room. The pyramid is regular and has a surface area of 105.35 square centimeters. Find the height of each triangular face. Justify your answer.

Surface area of pyramid = Area of base + area of lateral surfaces105.35cm2=12×7×6.1+3×12×7×hcm2105.35-21.35=3×12×7×h84=3×12×7×hh=8cmFinal answer: The height of pyramid is 8cm