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Calculating the areas of rectangles and triangles
You have learnt how to find the areas of rectangles and triangles by counting squares. However, sometimes you will have to calculate the areas of shapes without using a grid.
Rectangles
The formula for the area of a rectangle is:
Area = base x height.
The area of this rectangle is 72cm2 (12 x 6 = 72).
Triangles
To find the area of a triangle, you use the formula:
Area = 1/2 × base × height
Remember another way to find the area of a triangle, first make it into a rectangle, then divide by 2.
The area of this triangle is 20cm2:
1/2(10 × 4) = 20
Now try these questions.
- Question
Find the area of the following shape:
- Answer
The answer is 77cm2.
You need to multiply 7 by 11.
- Question
Find the area of the following shape:
- Answer
The answer is 14cm2.
If you had problems, remember that the rule is to multiply 7 by 4, then divide by 2.
More complex shapes
You have learnt how to find the area of a rectangle and a triangle. We are now going to look at finding the area of a more complex shape.
- Question
What is the area of this shape?
- Answer
The answer is 35cm2.
To find the area, you need to divide the shape into a rectangle and a triangle:
The area of the rectangle is 5 × 4 = 20cm2.
The base of the triangle is calculated by subtracting the base of the rectangle (4cm) from the total length of the shape (10cm). So 10cm - 4cm = 6cm.
The area of the triangle is 1/2(5 × 6) = 15cm2
The total area is 20 + 15 = 35cm2.
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