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Perimeters and Areas

10 min read

Perimeter and area

The perimeter is the distance around a shape. We measure it in length units such as cm or m. The area is the amount of surface inside a shape. We measure it in square units such as cm² or m².

Rectangles

A 6 by 4 rectangle holds 6 × 4 = 24 unit squares.
Rectangle with length l and width w.
Try itChange a rectangle

Make the rectangle longer or wider. Watch the perimeter and area. Can you find two rectangles with the same perimeter but different areas?

Triangles, parallelograms and trapeziums

Two identical triangles make a rectangle, so a triangle is half as big.
Area formulas
ShapeAreaNotes
Rectanglel × wlength times width
Triangle½ × b × hh is the perpendicular height
Parallelogramb × hh is the perpendicular height, not the slanted side
Trapezium½ × (a + b) × ha and b are the parallel sides
Area formulasFive shapes with their area formulas: rectangle length times width, triangle half base times height, parallelogram base times height, trapezium half the sum of the parallel sides times the height, and circle pi times radius squared.lwRectangleA = l × wbasehTriangleA = ½ × b × hbasehParallelogramA = b × habhTrapeziumA = ½(a + b) × hrCircleA = π r²
Try itArea of a triangle

Change the base and the height.

Worked exampleArea of a trapezium

A trapezium has parallel sides 5 cm and 9 cm and height 4 cm. Find its area.

  1. Use the formula.
  2. Substitute.

Answer: The area is 28 cm².

Circles

Parts of a circleA circle with its parts labelled: the centre, the radius from the centre to the edge, the diameter through the centre, a chord joining two points on the circle, an arc which is part of the circumference, a sector between two radii, a segment cut off by a chord, and a tangent touching the circle at one point.centreradiusdiametersectorchordarcsegmenttangent
The parts of a circle. The radius is half the diameter.
Circumference and area of a circle with radius r. Use π ≈ 3.14 or 22/7.
  • radius (centre to edge) (cm)
  • circumference (the perimeter of a circle)
Try itChange a circle

Make the radius bigger. When the radius doubles, the circumference doubles but the area becomes four times as big.

Check yourself A rectangle is 9 m long and 5 m wide. What is its perimeter?
Check yourself A triangle has base 10 cm and height 6 cm. What is its area?

Key terms

Perimeter
The distance around the outside of a shape.
Area
The surface inside a shape, in square units.
Circumference
The perimeter of a circle.
Perpendicular height
The height measured at a right angle to the base.

Summary

  • Perimeter is in cm, m, km; area is in cm², m², km².
  • Rectangle: P = 2(l + w), A = l × w.
  • Triangle: A = ½bh. Parallelogram: A = bh. Trapezium: A = ½(a + b)h.
  • Circle: C = 2πr and A = πr².
Coordinate Geometry