Question

The base of a prism is an equilateral triangle of perimeter 15 cm and its height is 10 cm. What is its total surface area ?

• A. $(150+\frac{20\sqrt{3}}{3})c{m}^2$
• B. $\left(\frac{300+25\sqrt{3}}{2}\right)c{m}^2$
• C. $\left(\frac{300+20\sqrt{3}}{2}\right)c{m}^2$
• D. None of these

Answer 1

The correct option is B

$\left(\frac{300+25\sqrt{3}}{2}\right)c{m}^2$

Perimeter =15 cm

For equilateral triangle: Perimeter = 3 $\times$ side

15 = 3 $\times$ s

s= 5 cm

Area of one triangular base = $\frac{\sqrt{3}}{4}{s}^2$

= $\frac{\sqrt{3}}{4}{5}^2$

= $\frac{25\sqrt{3}}{4}c{m}^2$

Area of both the triangular bases = $\frac{\text{/}2\times 25\sqrt{3}}{\text{/}{4}^2}$

= $\frac{25}{2}\sqrt{3}c{m}^2$

Lateral surface area of a prism = Perimeter $\times$ height = 15 $\times$ 10

= 150 $c{m}^2$

Now, Total surface area = Lateral surface area + area of both the triangular bases

= $(150+\frac{25\sqrt{3}}{2})c{m}^2$

= $\left(\frac{300+25\sqrt{3}}{2}\right)c{m}^2$