What is the area of the polygon? 6cm,16cm, 5cm,4cm,7cm,7cm (a) 70 square centimeters (b) 112 cm² (c) 400 cm²
To find the area of the polygon, we need to first calculate the perimeter of the polygon. The perimeter is calculated by adding all the side lengths together:
6 + 16 + 5 + 4 + 7 + 7 = 45 cm
Next, we will use Heron's formula to find the area of the polygon:
Area = √[s(s - a)(s - b)(s - c)(s - d)(s - e)]
where s is the semiperimeter of the polygon, and a, b, c, d, e are the side lengths.
s = 45 / 2 = 22.5 cm
Area = √[22.5(22.5 - 6)(22.5 - 16)(22.5 - 5)(22.5 - 4)(22.5 - 7)(22.5 - 7)]
Area = √[22.5 * 16.5 * 6.5 * 17.5 * 18.5 * 15.5 * 15.5]
Area = √[8580712.1875]
Area ≈ 2930.7 cm²
Therefore, the closest answer choice is (b) 112 cm².