Chapter 22

A rectangular tray is \(820 \mathrm{~mm}\) long and \(400 \mathrm{~mm}\) wide. Find its area in (a) \(\mathrm{mm}^{2}\), (b) \(\mathrm{cm}^{2}\), (c) \(\mathrm{m}^{2}\).

Find the areas of the circles having (a) a radius of \(5 \mathrm{~cm}\), (b) a diameter of \(15 \mathrm{~mm}\), (c) a circumference of \(70 \mathrm{~mm}\).

Calculate the areas of the following sectors of circles: (a) having radius \(6 \mathrm{~cm}\) with angle subtended at centre \(50^{\circ}\) (b) having diameter \(80 \mathrm{~mm}\) with angle subtended at centre \(107^{\circ} 42^{\prime}\) (c) having radius \(8 \mathrm{~cm}\) with angle subtended at centre \(1.15\) radians.

A hollow shaft has an outside diameter of \(5.45 \mathrm{~cm}\) and an inside diameter of \(2.25 \mathrm{~cm}\). Calculate the cross-sectional area of the shaft.

Calculate the area of a regular octagon, if each side is \(5 \mathrm{~cm}\) and the width across the flats is \(12 \mathrm{~cm}\).

Determine the area of a regular hexagon which has sides \(8 \mathrm{~cm}\) long.

A rectangular garage is shown on a building plan having dimensions \(10 \mathrm{~mm}\) by \(20 \mathrm{~mm}\). If the plan is drawn to a scale of 1 to 250 , determine the true area of the garage in square metres.