GCSE Perimeter and area Practice Questions

Write down the rule for the area of a rectangle.

The area of a rectangle is its length multiplied by its width.

Substitute the length and the width into the rule.

The rectangle is $8$ cm long and $5$ cm wide.

Work out the area of the rectangle.

The area is $40$ square centimetres.

Write down the rule for the area of a parallelogram.

Cutting a right-angled triangle off one end of a parallelogram and sliding it to the other end makes a rectangle of base $b$ and height $h$, so $A = bh$.

Pick out the perpendicular height, not the slanted side.

The slanted side of $6$ cm is longer than the perpendicular height and must not be used: $8 \times 6 = 48$ is the classic wrong answer here.

Select the correct area.

The area is $40$ square centimetres.

Write down how many centimetres make one metre.

There are $100$ centimetres in a metre.

Work out how many square centimetres make one square metre.

A square metre is a square $100$ cm by $100$ cm, so it holds $10000$ square centimetres. The conversion factor for area is the square of the one for length.

Multiply by that factor.

So $2$ square metres is $20000$ square centimetres.

Rule out the option that only multiplies by one hundred.

This uses the conversion factor for a length, not for an area — the standard mistake.

Check the size of the answer.

A square centimetre is much smaller than a square metre, so it takes many more of them to cover the same surface. The number must get much bigger.

Select the correct conversion.

$2$ square metres is $20000$ square centimetres.

Work out the area of rectangle A.

Rectangle $A$ has an area of $36$ square centimetres.

Write down the rule for the area of a triangle.

A triangle is half of a rectangle with the same base and the same perpendicular height, so $A = \frac{1}{2}bh$.

Work out the area of triangle B.

Triangle $B$ has an area of $30$ square centimetres, even though it has the longer base.

Subtract the smaller area from the larger.

Rectangle $A$ is $6$ square centimetres bigger than triangle $B$.

Rule out the statement that the areas are equal.

The two areas differ, so they cannot be equal.

Rule out the statements that make B the larger shape.

Triangle $B$ has the smaller area, so it cannot be greater than $A$ by any amount at all.

Rule out the wrong difference.

The gap between the two areas is $6$ square centimetres, not $12$ — that would be the difference between the rectangle and the triangle doubled.

Check the answer by comparing the triangle with its rectangle.

Forgetting to halve would have made triangle $B$ look like the bigger shape, which is exactly the trap here.

Check the difference the other way round.

Adding the difference back on to the smaller area gives $36$ square centimetres, so the gap really is that size.

Select the correct statement.

The area of $A$ is $6$ square centimetres greater than the area of $B$.

Write down the rule for the area of a triangle.

A triangle is half of a rectangle with the same base and the same perpendicular height, so $A = \frac{1}{2}bh$.

Write down the new base.

The base is doubled.

Write down the new perpendicular height.

The perpendicular height is halved.

Write down the new area.

Substitute the new base and the new height into the rule for the area of a triangle.

Simplify the new area.

The factor of $2$ and the factor of $\frac{1}{2}$ cancel each other out exactly.

Compare the new area with the old one.

The two areas are identical, so the area has not changed.

Test the result on a particular triangle.

Take a triangle with base $6$ cm and perpendicular height $8$ cm, of area $24$ square centimetres.

Change the triangle as the question says.

The new triangle has base $12$ cm and perpendicular height $4$ cm.

Work out the area of the new triangle.

The new area is $24$ square centimetres — exactly the same as before.

Work out the scale factor for the area.

The area is multiplied by $1$, which is another way of saying it is unchanged.

Rule out doubling and halving.

Neither $48$ nor $12$ is the new area, so the area is neither doubled nor halved.

Rule out the factor of four.

Neither $96$ nor $6$ is the new area either. A factor of $4$ would need both lengths to be doubled.

Explain why the two changes cancel.

The area depends on the product of the base and the height, and that product is unchanged when one is doubled and the other is halved.

Note what would change.

The triangle is now long and low rather than short and tall, so its perimeter has changed even though its area has not.

Select the correct statement.

The area is unchanged.