About Area
Every area formula is a variation on one length multiplied by another, and the questions are mostly about which lengths the formula actually wants. The commonest mistake in the topic is using base times height for a triangle and forgetting the half.
What you need to understand
- Area is measured in square units, so an answer given in centimetres rather than square centimetres is wrong.
- A triangle is half of a rectangle standing on the same base with the same height, and that is where the half comes from.
- Perimeter is a length and area is a surface. They are measured in different units and are never interchangeable.
- For a circle the radius and the diameter are not interchangeable, and using one for the other changes the area by a factor of four.
- Two shapes can share a perimeter and enclose different areas, so a perimeter never fixes an area.
- The area of a square of side s is s squared, while its perimeter is 4s.
Formulas to remember
How to work through these questions
- Write the formula down before substituting anything, and check which lengths it actually needs.
- Convert every length into the same unit first, because mixing centimetres with metres changes the area by a factor of ten thousand.
- If the perimeter of a square is given, divide by four to get the side before squaring it.
- For a circle, confirm whether the question gives the radius or the diameter before substituting.
- Check the units of the answer, because an area must come out in square units.
Mistakes that cost marks
- Forgetting to halve base times height when finding the area of a triangle.
- Using the diameter where the formula wants the radius, which multiplies the answer by four.
- Squaring the perimeter of a square instead of its side.
- Mixing units, such as a length in metres with a breadth in centimetres.
- Giving a perimeter when the question asked for an area.
Worked example
The perimeter of a square is 36 cm. Find its area.
- The side of a square is the perimeter divided by four, so the side is 36 / 4 = 9 cm.
- The area of a square is the side multiplied by itself.
- Area = 9 x 9 = 81 square cm.
- Check: a side of 9 cm is a sensible size for a perimeter of 36 cm, and the area of 81 is larger than the side length, as it must be.
Answer: 81 square cm
Practice questions with answers
A few Area questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A triangle has a base of 28 cm and a height of 11 cm. What is its area?
Answer: Option B — with explanation
Area of a triangle = \(\frac{1}{2}\) x base x height.
= \(\frac{1}{2}\) x 28 x 11 = 154 square cm.
Common mistakes
- used base x height and forgot to halve: 308
- added the base and the height: 39
- doubled the product instead of halving it: 616
Question 2
The radius of a circle is 28 cm. What is its area? (Take $\pi = \dfrac{22}{7}$)
Answer: Option C — with explanation
Area of a circle = $\pi r^{2}$.
= $\dfrac{22}{7} \times 28 \times 28$ = 2464 square cm.
Common mistakes
- gave the circumference instead of the area: 176
- halved r squared instead of using it whole: 1232
- used the radius once instead of squaring it: 88
Question 3
Calculate the area of a triangle with base 4 cm and perpendicular height 20 cm.
Answer: Option A — with explanation
Area of a triangle = \(\frac{1}{2}\) x base x height.
= \(\frac{1}{2}\) x 4 x 20 = 40 square cm.
Common mistakes
- doubled the product instead of halving it: 160
- added the base and the height: 24
- used base x height and forgot to halve: 80
Question 4
Calculate the area of a circle of radius 49 cm, taking $\pi = \dfrac{22}{7}$.
-
A
154
-
B
308
-
C
3773
-
D
7546
Answer: Option D — with explanation
Area of a circle = $\pi r^{2}$.
= $\dfrac{22}{7} \times 49 \times 49$ = 7546 square cm.
Common mistakes
- halved r squared instead of using it whole: 3773
- gave the circumference instead of the area: 308
- used the radius once instead of squaring it: 154
Question 5
Calculate the area of a triangle with base 22 cm and perpendicular height 19 cm.
Answer: Option C — with explanation
Area of a triangle = \(\frac{1}{2}\) x base x height.
= \(\frac{1}{2}\) x 22 x 19 = 209 square cm.
Common mistakes
- used base x height and forgot to halve: 418
- doubled the product instead of halving it: 836
- added the base and the height: 41
Frequently asked questions
Why is the area of a triangle half of base times height?
Because a triangle is exactly half of a rectangle drawn on the same base with the same height. Two identical triangles fit together to make that rectangle.
How do I find the area of a circle?
Multiply pi by the square of the radius. With pi as 22/7 and a radius of 7 cm, the area is (22/7) x 49 = 154 square cm.
What is the difference between area and perimeter?
Perimeter is the distance around the edge and is measured in centimetres. Area is the surface enclosed and is measured in square centimetres. A shape has both, and neither one determines the other.
Can two rectangles have the same perimeter but different areas?
Yes. A 6 by 4 rectangle and a 7 by 3 rectangle both have a perimeter of 20, but their areas are 24 and 21 square cm.
