Maths
Area
The area of a shape is a measure of the 2 dimensional space that it covers. Area is measured in squares - eg square cm, square metres and square km.
This Revision Bite covers:
A square cm has a length of 1 cm. We say that it has an area of 1 cm^{2} ( 1 cm squared).
This rectangle contains six squares. Each of the squares has an area of 1cm^{2}, so the area of the rectangle is 6cm^{2}.
By counting the squares, find the area of the following shapes:
a)
b)
a) 10cm^{2}
b) 8cm^{2}
Remember, there are six whole squares and four half squares in the triangle.
Another way to find the area of a rectangle is to multiply its length by its width.
The formula is: area = length × width
We can rearrange this formula to find the length or the width:
length = area ÷ width
width = area ÷ length
What is the length of this rectangle?
The area is 56cm^{2} and the width is 7cm, so the length is 56 ÷ 7 = 8cm
Look at the triangle below:
If you multiply the base by the perpendicular height, you get the area of a rectangle. The area of the triangle is half the area of the rectangle.
So to find the area of a triangle, multiply the base by the perpendicular height and divide by two. The formula is:
Area = ^{(b × h)}/_{2}
Find the area of this triangle:
The area of the triangle is:
^{(5 × 8)}/_{2} = ^{40}/_{2} = 20cm^{2}
There are two different methods for finding the area of this shape:
Divide the shape into squares and rectangles, find their individual areas and then add them together.
Area = 16 + 16 + 48 = 80cm^{2}
Imagine the shape as a large rectangle with a section cut out.
Find the area of the large rectangle (12 × 8) and then subtract the part that has been cut out (4 × 4)
Area = (12 × 8) - (4 × 4) = 96 - 16 = 80cm^{2}
The area of a parallelogram is the base × perpendicular height (b × h).
You can see that this is true by rearranging the parallelogram to make a rectangle.
Use the perpendicular height of the parallelogram, not the sloping height.
Find the area of this parallelogram:
The answer is 21cm^{2}.
Remember to use the perpendicular height.
You now know how to find the area of a parallelogram, but what happens if you need to find the base or the height? You just have to rearrange the formula.
A = b × h
h = A ÷ b
b = A ÷ h
Q1. The area of this parallelogram is 12cm^{2}. What is its perpendicular height?
Q2. Find the length of the base of this parallelogram:
A1. h = A ÷ b
h = 12 ÷ 4 = 3cm
A2. b = A ÷ h
b = 40 ÷ 5 = 8cm
Remember to divide the area by the perpendicular height.
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