Perimeter and Area of Rectangles and Triangles
Perimeter is the total distance around the outside of a 2D shape, found by adding together the lengths of every side. The area of a rectangle is found by multiplying its length by its width, and the area of a triangle is found using area = 1/2 x base x perpendicular height, where the height must be measured at right angles to the chosen base rather than along a slanting side.
Method
- For perimeter, add together the lengths of every side of the shape, making sure all lengths are given in the same unit first.
- For the area of a rectangle, multiply the length by the width.
- For the area of a triangle, identify the base and the perpendicular height, which must be at right angles to that base rather than a slanted side.
- Use the formula area = 1/2 x base x height for a triangle.
- For a compound shape, split it into rectangles and triangles you can find the area of separately, then add (or subtract) the parts as needed.
- Always give your final answer with the correct unit: length in cm or m, area in cm^2 or m^2.
Worked example
A rectangle has length 12 cm and width 7 cm. A right-angled triangle sits on top of it, with the same base of 12 cm and a perpendicular height of 5 cm. Find (a) the area of the rectangle, (b) the area of the triangle, (c) the total area of the combined shape.
- Area of the rectangle = length x width = 12 x 7 = 84 cm^2.
- Area of the triangle = 1/2 x base x height = 1/2 x 12 x 5 = 30 cm^2.
- Total area = area of rectangle + area of triangle = 84 + 30 = 114 cm^2.
Practice questions
Try each question, then tap to reveal the answer.
Q1Find the area of a rectangle with length 9 cm and width 4 cm.Show answer
Answer: 9 x 4 = 36 cm^2
Q2Find the perimeter of a rectangle with length 15 cm and width 6 cm.Show answer
Answer: 2(15 + 6) = 42 cm
Q3Find the area of a triangle with base 10 cm and height 6 cm.Show answer
Answer: 1/2 x 10 x 6 = 30 cm^2
Q4A square has a side length of 8 cm. Find its area and its perimeter.Show answer
Answer: Area = 8 x 8 = 64 cm^2, perimeter = 4 x 8 = 32 cm
Q5A triangle has an area of 24 cm^2 and a base of 8 cm. Find its height.Show answer
Answer: Height = (2 x 24) / 8 = 48 / 8 = 6 cm
Q6A rectangle has an area of 45 cm^2 and a width of 5 cm. Find its length.Show answer
Answer: Length = 45 / 5 = 9 cm
Q7Find the perimeter of a right-angled triangle with a base of 6 cm, a height of 8 cm, and a hypotenuse of 10 cm.Show answer
Answer: 6 + 8 + 10 = 24 cm
Q8A rectangular lawn measures 20 m by 12 m. Find its area.Show answer
Answer: 20 x 12 = 240 m^2
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A triangle has a base of 14 cm and a perpendicular height of 9 cm. Work out its area, stating the correct unit.
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A garden is made up of a rectangle measuring 10 m by 6 m, with a triangular flower bed removed from one corner. The flower bed is a right-angled triangle with a base of 4 m and a height of 3 m. Work out the remaining area of the garden after the flower bed is removed.
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Free printable worksheet
Want more practice on paper? Download the perimeter and area of rectangles and triangles worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 7 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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