Quadrilaterals for OCR GCSE Maths
This page covers the following topics:
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.
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.
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.
Sketch a rhombus, depicting its properties.
Describe what is meant by perpendicular bisectors.
Two lines are perpendicular bisectors if they are perpendicular to each other and bisect each other.
Find the value of x.
2x + x + 110 + 70 = 360º, therefore 3x = 180 and x = 60º.
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