Area units questions with answers

Questions

1. Question 1m² to cm²

   Express $7.25$ m² in cm².

   Show the worked solution

   1. Step 1: 1 m = 100 cm, so square it for area$1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}$$= 10\,000 \text{ cm}^2$
   2. Step 2: Change to cm²: multiply or divide?$7.25 \text{ m}^2 = 7.25 \times 10\,000 \text{ cm}^2$$= 72\,500$ cm²
2. Question 2cm² to m²

   A notice board has an area of $9000$ cm². Express this area in m².

   Show the worked solution

   1. Step 1: 1 m = 100 cm, so square it for area$1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm}$$= 10\,000 \text{ cm}^2$
   2. Step 2: Change to m²: multiply or divide?$9000 \text{ cm}^2 = \dfrac{9000}{10\,000} \text{ m}^2$$= 0.9$ m²
3. Question 3Lengths in different units

   The diagram shows a rectangular carpet measuring $2.5$ m by $90$ cm. Find its area, in cm².

   Show the worked solution

   1. Step 1: Change both lengths to centimetres first$2.5 \text{ m} = 2.5 \times 100 \text{ cm}$$= 250 \text{ cm}$
   2. Step 2: Area = length × breadth$\text{Area} = 250 \times 90$$= 22\,500$ cm²
4. Question 4Covering a floor with tiles

   The floor of a patio is a rectangle measuring $3.6$ m by $2.4$ m. It is covered completely with square tiles of side $30$ cm. Find the number of tiles needed.

   Show the worked solution

   1. Step 1: Change the floor's lengths to centimetres$3.6 \text{ m} = 360 \text{ cm}$$2.4 \text{ m} = 240 \text{ cm}$
   2. Step 2: How many tiles fit along each side?$\dfrac{360}{30} = 12$ tiles along the length$\dfrac{240}{30} = 8$ tiles along the breadth
   3. Step 3: Multiply$\text{Number of tiles} = 12 \times 8$$= 96$
5. Question 5Hectares and km²

   A nature reserve has an area of $3$ ha. Express this area in m². (1 hectare $= 10\,000$ m²)

   Show the worked solution

   1. Step 1: Change to m²: multiply or divide?$3 \text{ha} = 3 \times 10\,000 \text{m}^2$$= 30\,000$ m²