Area (OCR GCSE Maths): Revision Notes

Example:

• Given: A rectangle with a base of $3$ cm and a height of $9$ cm.

  

• Calculation:

• Answer: The area of the rectangle is $27 \ cm^2$. Steps:

1. Identify the base $b$ and height $h$ of the rectangle.
2. Multiply the base by the height.
3. The result is the area in squared units.

Example:

• Given: A triangle with a base of $10$ m and a perpendicular height of $12$ m.

  

• Calculation:

• Answer: The area of the triangle is $60 \ m^2$. Steps:

4. Identify the base $b$ and the perpendicular height $h$ of the triangle.
5. Multiply the base by the height.
6. Divide the result by $2$ to find the area in squared units.

Example:

• Given: A parallelogram with a base of $5$ mm and a perpendicular height of $10$ mm.

  

• Calculation:

• Answer: The area of the parallelogram is $50 \ mm^2$. Steps:

7. Identify the base $b$ and the perpendicular height $h$.
8. Multiply the base by the height.
9. The result gives the area in squared units.

Example:

• Given: A trapezium with parallel sides measuring $2.8$ cm and $4.2$ cm, and a height of $8$ cm.

  

• Calculation:

• Answer: The area of the trapezium is $28 \ cm^2$. Steps:

10. Add the lengths of the parallel sides $p$ and $q$.
11. Divide the sum by $2$ to get the average length of the base.
12. Multiply the average base length by the height $h$.
13. The result is the area in squared units.

Example:

• Given: A kite with diagonals of $2.5$ m and $4$ m.

  

• Calculation:

• Answer: The area of the kite is $5 \ m^2$. Steps:

14. Measure or identify the lengths of the diagonals $d₁$ and $d₂$.
15. Multiply these lengths together.
16. Divide the product by $2$ to get the area in squared units.

Example:

• Given: A circle with a diameter of $12.6\ m$.

  

• Calculation:

• First, find the radius: $r=\frac{12.6 m}2=6.3\ m.$

• Answer: The area of the circle is approximately $124.7 \ m^2$. Steps:

17. If given the diameter, halve it to find the radius $r$.
18. Square the radius $r^2$.
19. Multiply the squared radius by $π$ to find the area in squared units.

Worked Example: Finding the Area of a Compound Shape

Problem: You are given a compound shape made up of a rectangle and a trapezium. You need to find the total area of the shape.

Step 1: Identify and Split the Compound Shape

The shape can be divided into:

20. Rectangle
21. Trapezium

Step 2: Calculate the Area of Each Shape

1. Rectangle (Shape $1$)

Given:

• Base $b=7 \ mm$
• Height $h=11 mm$

Formula:

Calculation:

2. Trapezium (Shape $2$) Given:

• Parallel sides $p=20 mm$ and $q=7 mm$
• Height $h=12 mm$

Formula:

Calculation:

$Area=\frac{(20\ mm+7\ mm)}2×12 \ mm=\frac{27 \ mm}2×12\ mm=13.5 \ mm×12\ mm=162 \ mm^2$

Step 3: Add the Areas Together

Total Area:

Answer: The total area of the compound shape is $239 \ mm^2$.

Worked Example: Calculating Surface Area

Let's consider a $3D$ object that is composed of several simpler shapes. The task is to calculate the total surface area of this object.

Step 1: Identify and Label Each Face

Break the 3D object into simpler $2D$ shapes:

3. Triangle (Shape $1$)
4. Rectangle (Shape $2$)
5. Rectangle (Shape $3$)
6. Rectangle (Shape $4$)
7. Triangle (Shape $5$)

Step 2: Calculate the Area of Each Face

8. Triangle (Shape $1$)

• Given: Base $b=6 cm$, Height $h=8 cm$
• Formula:

• Calculation:

9. Rectangle (Shape $2$)

• Given: Length $l=10 cm$, Width $w=2 cm$
• Formula:

• Calculation:

10. Rectangle (Shape $3$)

• Given: Length $l=2 cm$, Width $w=6 cm$
• Formula:

• Calculation:

11. Rectangle (Shape $4$)

• Given: Length $l=8 cm$, Width $w=2 cm$
• Formula:

• Calculation:

12. Triangle (Shape $5$)

• Given: This triangle is the same as Shape $1$.
• Area:

Step 3: Add the Areas Together

Total Surface Area:

Answer: The total surface area of the shape is $96\ cm^2$.