StudySquare
Quadrilaterals for Edexcel GCSE Maths






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 90º 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.

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

A trapezium is a quadrilateral with one pair of opposite parallel sides. The sum of the interior angles of a trapezium is 360º. 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.

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 360º. The diagonals of a kite bisect each other perpendicularly.

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 360º. The diagonals of a rhombus bisect each other perpendicularly.

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 cm².

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.
3
Sketch a rhombus, depicting its properties.
image

4
Describe what is meant by perpendicular bisectors.
Two lines are perpendicular bisectors if they are perpendicular to each other and bisect each other.
5
Find the value of x.
2x + x + 110 + 70 = 360º, therefore 3x = 180 and x = 60º.

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