What will be the total surface area of the symmetrical pyramid having a square base with an area of 576 \( m^2\) and height 5 m?
Answer
Correct Answer : a ) A) \({1200 m^2}\)
Explanation :Given:
Height (H) = 5 m
Area of square base =\(576 m^2\)
So, Side of the square, a = \( \sqrt{576} \) = 24 m
Now,
The lateral height of the triangle, L
L = \(\sqrt{H^2+{(\frac{a}{2}})^2}\)
L = \(\sqrt{5^2+{(\frac{24}{2}})^2}\)
L = 13m
There are 4 symmetrical triangles in the pyramid so, the total surface area of the pyramid is
= 4 x (area of triangles) + area of base
= \(4*(\frac{1}{2}*base*height)+576\)
=\(4*(\frac{1}{2}*24*13)+576\)
= 624 + 576
= \(1200 m^2\)
Hence, (a) is the correct answer.
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