Areas (2D Mensuration)

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Quick recall

• Area uses square units; circumference uses linear units.
• Height is perpendicular to the base; use the specified value of pi.

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Formula Cards

1. Triangle

$$A=\frac{1}{2}bh$$

h is perpendicular height.

2. Rectangle

$$A=lw$$

3. Square

$$A=s^2$$

4. Circle area

$$A=\pi r^2$$

5. Circle circumference

$$C=2\pi r$$

6. Parallelogram

$$A=bh$$

7. Trapezium

$$A=\frac{1}{2}(a+b)h$$

a and b are parallel sides.

8. Rhombus

$$A=\frac{1}{2}d_1d_2$$

d₁ and d₂ are diagonals.

Worked Examples

Example 1

Question: Find the area of a circle of radius 7 units.

Step 1: Square the radius.

$$r^2=7^2=49$$

Step 2: Multiply by pi.

$$A=49\pi$$

Answer: 49π square units; 154 if π = 22/7.

Example 2

Question: A trapezium has parallel sides 8 and 12 units and height 5 units. Find its area.

Step 1: Add the parallel sides.

$$8+12=20$$

Step 2: Multiply by half the height.

$$A=\frac{1}{2}(20)(5)=50$$

Answer: 50 square units.

Example 3

Question: A rhombus has diagonals 10 and 12 units. Find its area.

Step 1: Multiply the diagonals.

$$10\times12=120$$

Step 2: Halve the product.

$$A=\frac{120}{2}=60$$

Answer: 60 square units.

Example 4

Question: A triangle has base 10 units and perpendicular height 6 units. Find its area.

Step 1: Multiply base and height.

$$10\times6=60$$

Step 2: Halve the product.

$$A=30$$

Answer: 30 square units.

Drill

Try each question before opening its answer.

Question 1

Area of a circle with r=14.

• Show answer

  616 (using π=22/7)

Question 2

Area of a rectangle 12×5.

• Show answer

  60

Question 3

Area of a trapezium, parallel sides 6 & 10, height 4.

• Show answer

  32

Question 4

Area of a rhombus with diagonals 8 and 6.

• Show answer

  24

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