Area:  Finding the area of common shapes

Levels 5-7

 

 

The objectives of this unit are to find the area of shapes involving:

*  rectangles;

*  triangles;

*  parallelograms;

*  trapeziums.

 

The area of a shape is measured in square units, such as cm², m², or mm².  It is important that all lengths on a shape are converted to the same unit before its area can be found.

 

 

 

 

Example 1:

Find the area of this shape:

 

 

 

 

 

 

 

 

 

Solution:  We can split this shape up into 2 rectangles.  One way of doing this is as follows:

 

 

 

 

 

 

 

 

 

 

 

 

 

* * * * *

 

 

Note:  The measurements used for the base and the height must be perpendicular (i.e. at right angles) to each other.

 

Example 2:

Find the area of this parallelogram-

 

 

 

 

 

 

 

Solution:  To find the area, we need two measurements that are perpendicular to each other.  Here we see that the base is 6.8 cm and the height is 4.3 cm.

 

So area = 6.8 × 4.3 = 29.24 cm².

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Example 3:

Work out the length of the missing side.

 

 

 

 

 

 

 

 

Solution: 

The measurements 12cm and 4cm are perpendicular to each other and so can be used to find the area of the parallelogram: 

                                    area = 12 × 4 = 48cm²

Another way to find the area of the parallelogram would be to multiply 8cm by the unknown height.

So

                                    8 × ? = 48

                                          ? = 48 ÷ 8

                                          ? = 6cm

 

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Example 4:

Find the area of the triangle shown:

 

 

 

 

 

 

 

 

Solution:

Area =

 

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Example 5:

The triangle shown has an area of 36 cm².  Find the height of the triangle.

 

 

 

 

 

 

 

 

Solution:

Recall that a triangle has an area that is half of the surrounding rectangle.

Therefore the area of the rectangle shown below must be 72cm².

 

 

 

 

 

 

 

 

The rectangle has length 9cm and width ?cm.

                        So  72 = 9 × ?

                                 ? = 72 ÷ 9 = 8cm

The triangle has height 8 cm.

 

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Example 6:

Find the area of the trapezium shown below:

 

 

 

 

 

 

Solution:

Using the formula:        

So:                                                 (working out the value of the brackets)

So:                              

 

OR using the steps:

Step 1: Add together the parallels sides 13 + 17 = 30

Step 2:  Multiply by the height:              30 × 6.5 = 195

Step 3:  Divide by 2:                                         195 ÷ 2 = 97.5 cm².

 

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Example 7:

Find the area of the shape shown here:

 

 

 

 

 

 

 

 

 

 

Solution:

Area of the trapezium is           

                                                                          =

 

Area of the triangle is               

 

So total area of the shape is 152 + 96 = 248cm²

 

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