The perimeter of a semi-circular metallic plate is 86.4 cm. Calculate the radius and area of the plate.

Perimeter of semicircular plate = Circumference of semicircle + diameter

= πr + 2r

= r(π + 2).

Thus,

$\Rightarrow 86.4 = r(π + 2) \\[1em] \Rightarrow r = \dfrac{86.4}{π + 2} \\[1em] \Rightarrow r = \dfrac{86.4}{3.14 + 2} \\[1em] \Rightarrow r = \dfrac{86.4}{5.14} \approx 16.8 \text{ cm}.$

Area of semi-circular plate = $\dfrac{1}{2}$ πr²

= $\dfrac{1}{2}$ × 3.14 × (16.8)²

= 443.12 cm².

Hence, radius of plate = 16.8 cm and area = 443.12 cm².