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Quadrilaterals for OCR GCSE Maths

Quadrilaterals

This page covers the following topics:

1. Squares
2. Rectangles
3. Trapezia
4. Kites
5. Rhombi

A square is a quadrilateral with four equal sides and four 90ยบ angles. The diagonals of a square bisect each other and are perpendicular to each other, therefore they are perpendicular bisectors. The diagonals of a square are equal to each other. Opposite sides of a square are parallel.

Squares

A rectangle is a quadrilateral with four 90ยบ interior angles and opposite sides which are equal and parallel. The diagonals of a rectangle bisect each other.

Rectangles

A trapezium is a quadrilateral with one pair of opposite parallel sides. The sum of the interior angles of a trapezium is 360ยบ. The area of a trapezium can be calculated using the following formula: (a + b)h/2, where h is the perpendicular height of the trapezium, and a and b are its opposite parallel sides.

Trapezia

A kite is a quadrilateral with two pairs of equal sides and one pair of equal angles. The sum of the interior angles of a kite is 360ยบ. The diagonals of a kite bisect each other perpendicularly.

Kites

A rhombus is a quadrilateral with four equal sides, where opposite sides are parallel, and two pairs of opposite, equal angles. The sum of the interior angles of a rhombus is 360ยบ. The diagonals of a rhombus bisect each other perpendicularly.

Rhombi

1

Given that a is 20 cm, b is 22 cm and h is 13 cm in the given diagram, calculate the area of the trapezium.

Area = (20 + 22)(13)/2 = 273 cmยฒ.

Given that a is 20 cm, b is 22 cm and h is 13 cm in the given diagram, calculate the area of the trapezium.

2

How is a rhombus different to a trapezium?

A trapezium only has one pair of parallel sides, whereas a rhombus has two pairs of parallel sides which are also equal.

How is a rhombus different to a trapezium?

3

Sketch a rhombus, depicting its properties.

image

Sketch a rhombus, depicting its properties.

4

Describe what is meant by perpendicular bisectors.

Two lines are perpendicular bisectors if they are perpendicular to each other and bisect each other.

Describe what is meant by perpendicular bisectors.

5

Find the value of x.

2x + x + 110 + 70 = 360ยบ, therefore 3x = 180 and x = 60ยบ.

Find the value of x.

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