Note: Use Q1-5 from GCSE areas of shapes.
Areas of Shapes FSQ6
An architect designs a house with the following ground-floor plan:
Areas of Shapes FS6(a)
Calculate the area of the living room.
Answer type: simple
Answer: 20 m^2
Workings:
4\times5=20 m^2
1 mark
Areas of Shapes FS6(b)
Calculate the area of the bathroom.
Answer type: simple
Answer: 9 m^2
Workings:
3\times3=9 m^2
1 mark
Areas of Shapes FS6(c)
Calculate the area of the kitchen-diner.
Answer type: simple
Answer: 26 m^2
Workings:
Splitting the kitchen-diner into two rectangular compartments:
The total area is the sum of the areas of the two compartments:
Area =4\times5+3\times2=26 m^2
2 marks
Areas of Shapes FS6(d)
Calculate the area of the entire ground floor.
Answer type: simple
Answer: 55 m^2
Workings:
20+9+26=55 m^2
1 mark
Areas of Shapes FSQ7
Below is a compound shape consisting of a semi-circle, a rectangle and a right-angled triangle.
Calculate the area of the compound shape.
Give your answer to 2 decimal places.
You should use a value of \pi = 3.14
Answer type: simple
Answer: 58.12 m^2
Workings:
First, calculate the area of the individual shapes:
Area of semicircle =\dfrac{\pi r^2}{2} = \dfrac{3.14\times4^2}{2}=\dfrac{50.24}{2}=25.12 m^2
Area of rectangle =8\times3=24 m^2
Area of triangle =0.5\times base \times height =0.5\times6\times3=9 m^2
Thus,
Total area =25.12+24+9=58.12 m^2
4 marks