Exam-Style Questions.

The diagram below shows two rectangles not drawn to scale.

The perimeter of rectangle EFGH is 41cm and the area of rectangle ABCD is 55cm².

• EF = 9.5cm
• AB = FG

Find the length of AD.

Worked Solution

Find the value of \(x\).

Worked Solution

Walter Wall is planning to renovate a remote building by installing new flooring. A diagram showing the area required to be covered by the flooring can be seen below.

ABCDEFG is a regular heptagon with sides of length 5m.

O is the centre of the heptagon and M is the midpoint of AB.

(a) Find angle AOM

(b) Calculate the area of the heptagon in square metres.

Walter may be able to save money by purchasing some second-hand flooring material in the shape of a circle.

(c) Find the area of the circle that passes through the vertices of the heptagon.

Worked Solution

A red square has sides of length \(x\) cm. A blue rectangle has sides of length \(3x-1\) cm and \(x-2\) cm. The diagrams below are not drawn to scale.

The area of the rectangle is \(132\) cm² greater than the area of the square.

The difference between the perimeters of the two shapes is \(p\) cm.

Find the value of \(p\).

You must show all your working.

Worked Solution

Find the length of the sides of a square from the following clues:

• The square is drawn inside a circle.
• Each vertex of the square lies on the circumference of the circle.
• The area of the circle is 64cm².

Give your answer in centimetres to three significant figures.

Worked Solution

Five identical circles fit exactly inside a rectangle as shown in the diagram.

Find the area of the rectangle in terms of \(r\), the radius of the circles.

Worked Solution

Two identical small yellow circles are drawn inside one large circle, as shown in the diagram. The centres of the small circles lie on the diameter of the large circle. The part of the large circle that is outside both small circles is painted red.

Find the fraction of the large circle that is painted red.

Worked Solution