Area

Calculate area of triangles, quadrilaterals and composite shapes.

Measurement · MA4-ARE-C-01

Sub-topics

Area of rectangles and triangles

Calculate the area of rectangles, squares and triangles, and find the area of composite shapes made from these.

Area of composite shapes

Find the area of composite shapes by splitting them into rectangles, triangles and semicircles.

Open Math

Area

Measurement · MA4-ARE-C-01

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Area of rectangles and triangles

Q1Straightforward

A rectangle has a length of

8

cm and a width of

5

cm. What is its area in cm²?

Q2Straightforward

A square has a side length of

7

m. What is its area in m²?

Q3Straightforward

A rectangle has a length of

12

cm and a width of

3

cm. What is its area in cm²?

Q4Straightforward

A rectangle has a length of

9

m and a width of

6

m. What is its area in m²?

Q5Moderate

A triangle has a base of

10

cm and a perpendicular height of

6

cm. What is its area in cm²?

Q6Moderate

A triangle has a base of

8

m and a perpendicular height of

7

m. What is its area in m²?

Q7Moderate

A triangle has a base of

14

cm and a perpendicular height of

5

cm. What is its area in cm²?

Q8Moderate

A triangle has a base of

9

m and a perpendicular height of

12

m. What is its area in m²?

Q9Challenging

A composite shape is made of a rectangle

10

cm long and

4

cm tall with a triangle on top. The triangle has a base of

10

cm and a height of

3

cm. What is the total area in cm²?

Q10Challenging

A composite shape is made of a rectangle

8

m wide and

5

m tall with a triangle on top. The triangle has a base of

8

m and a height of

4

m. What is the total area in m²?

Q11Challenging

A composite shape is made of a rectangle

9

cm long and

4

cm wide. A right triangle with a base of

6

cm and a height of

4

cm is attached to one end of the rectangle. What is the total area in cm²?

Q12Challenging

A composite shape is made of a square with side length

6

cm and a triangle attached to one side. The triangle has a base of

6

cm and a height of

5

cm. What is the total area in cm²?

Area of composite shapes

Q13Straightforward

An L-shaped figure is formed by taking a

10 \text{ m} \times 6 \text{ m}

rectangle and removing a

4 \text{ m} \times 2 \text{ m}

rectangle from one corner. Find the area in m².

Q14Straightforward

A composite shape is made of two rectangles joined together. One rectangle measures

7 \text{ cm} \times 3 \text{ cm}

and the other measures

4 \text{ cm} \times 5 \text{ cm}

. Find the total area in cm².

Q15Straightforward

An L-shaped figure is formed by taking a

12 \text{ cm} \times 5 \text{ cm}

rectangle and removing a

3 \text{ cm} \times 4 \text{ cm}

rectangle from one corner. Find the area in cm².

Q16Straightforward

A step-shaped figure consists of two rectangles. The upper rectangle measures

8 \text{ m} \times 2 \text{ m}

and the lower rectangle measures

5 \text{ m} \times 3 \text{ m}

. Find the total area in m².

Q17Moderate

A composite shape is formed by a

12 \text{ cm} \times 5 \text{ cm}

rectangle with a triangle of base

12 \text{ cm}

and height

4 \text{ cm}

removed from the top edge. Find the remaining area in cm².

Q18Moderate

A composite shape consists of an

8 \text{ m} \times 6 \text{ m}

rectangle with a triangle of base

4 \text{ m}

and height

6 \text{ m}

attached to one end. Find the total area in m².

Q19Moderate

9 \text{ cm} \times 4 \text{ cm}

rectangle has a right triangle with base

3 \text{ cm}

and height

4 \text{ cm}

removed from one corner. Find the remaining area in cm².

Q20Moderate

A composite shape is formed by a

10 \text{ m} \times 5 \text{ m}

rectangle with a triangle of base

10 \text{ m}

and height

3 \text{ m}

placed on top. Find the total area in m².

Q21Challenging

A composite shape is formed by a

10 \text{ cm} \times 6 \text{ cm}

rectangle with a semicircle of diameter

6 \text{ cm}

attached to one of the shorter ends. Find the total area to 2 decimal places in cm².

Q22Challenging

A square with side length

10 \text{ m}

has a semicircle of diameter

10 \text{ m}

removed from one side. Find the remaining area to 2 decimal places in m².

Q23Challenging

A composite shape is formed by an

8 \text{ cm} \times 5 \text{ cm}

rectangle with a semicircle of diameter

8 \text{ cm}

attached to one of the longer sides. Find the total area to 2 decimal places in cm².

Q24Challenging

A stadium-shaped figure is formed by a

6 \text{ m} \times 4 \text{ m}

rectangle with a semicircle of diameter

4 \text{ m}

attached to each of the shorter ends. Find the total area to 2 decimal places in m².

Worked solutions and answers at openmath.au/year-7/area