SSC Selection Post 2020 PYQ — Question 65

The correct answer is option 4 i.e. 702$1\over4$π.

a = 28 cm , b = 45 cm , c = 53 cm

ΔR = $\frac{abc}{4\Delta}$

Heron’s formula :

$s = \frac{a + b + c}{2} = \frac{28 + 45 + 53}{2} = \frac{126}{2} = 63$

$\Delta = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{63(63 - 28)(63 - 45)(63 - 53)} = \sqrt{63 \cdot 35 \cdot 18 \cdot 10}$

$\Delta = \sqrt{63 \cdot 35 \cdot 18 \cdot 10} = \sqrt{396900} = 630$ cm²

R = $\frac{abc}{4\Delta} = \frac{28 \cdot 45 \cdot 53}{4 \cdot 630}$

R = $\frac{66780}{2520} = 26.5$  cm

Area = $\pi R^2 = \pi \cdot (26.5)^2 = \pi \cdot 702.25$ $\approx702\frac{1}{4}\pi$