Discussion

Question:

What is the area (in cm²) of a cyclic quadrilateral with sides 62 cm, 51 cm, 38 cm, and 23 cm?

Explanation:

The given quadrilateral is a cyclic quadrilateral.

Area of a cyclic quadrilateral = $\surd \left(\right(s-a\left)\right(s-b\left)\right(s-c\left)\right(s-d) )$

where s is the semi perimeter of the cyclic quadrilateral and is given as s = (a + b + c + d)/2

s = (62+51+38+23)/2 = 87 cm

Area of □ABCD = $\surd \left(\right(87-62\left)\right(87-51\left)\right(87-38\left)\right(87-23) )$

= $\surd (25\times 36\times 49\times 64)$ = 5 × 6 × 7 × 8 = 1680 cm2.

Hence, option (a).

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