# QOTD-Quantitative Aptitude- Mensuration

2019-07-21 | Team PendulumEdu

**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 \(m\)?**

** A)** \({1200 m^2}\)

**B)** \(956 m^2\)

**C)** \(1050 m^2\)

**D)** \(1100 m^2\)

**Correct answer (A)**

**Solution**

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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