Perimeter, Area, Volume and Surface Area: Practice Questions

What is the area of a triangle if the base is \( 20 \text{ cm} \) and the height is \( 7 \text{ cm} \)?

In the figure, \( ABCD \) is a trapezoid where \( AB \parallel DC \). Given that \( AB = 8 \text{ cm} \), \( DC = 12 \text{ cm} \), and the height of the trapezoid is \( 5 \text{ cm} \), find its area.

A regular hexagon and an equilateral triangle have exactly the same perimeter. If the area of the equilateral triangle is \( A \), find the area of the regular hexagon in terms of \( A \).

A triangle has a base of \( 6 \text{ cm} \) and a height of \( 4 \text{ cm} \). What is its area?

In a circle with a radius of \( 7 \text{ cm} \), find the perimeter of a sector that has a central angle of \( 60^\circ \). (Take \( \pi \approx \frac{22}{7} \))

A rectangle has a perimeter of \( 40 \text{ cm} \). If the length of the rectangle is \( 4 \text{ cm} \) longer than its width, find the area of the rectangle.

The figure shows the layout of a playground. Using the dimensions provided in the figure, answer the following questions:

(a) Calculate the total perimeter of the playground. Give your answer correct to \( 2 \) decimal places.

(b) Calculate the total area of the playground. Give your answer correct to \( 2 \) decimal places.

(Take \( \pi = 3.14 \))