Question 1
The diagram shows a plan of some cardboard packaging.
Calculate the total area of the cardboard used in cm^2 to 1 d.p..
ANSWER: Simple Text Answer
Answer: 111.5
Workings:
We can calculate the area of the rectangle ABCD as Area = 5\times 7 = 35 cm^2.
We can calculate the area of rectangle CEFG as Area = 6\times 9 = 54 cm^2.
We can calculate the area of the triangle CDG as Area = \dfrac{1}{2}\times 5\times 9 = 22.5 cm^2.
Total Area = 35 + 54 + 22.5 = 111.5 cm^2
Marks = 3
Question 2
The diagram shows the floor plan of a storeroom
The owner has ordered 14 items that each need at least 200 cm^2 of floor space.
CD=15 cm\\ CA=45 cm\\ AB=100 cm\\ FE=15 cm\\ EB=10cm
Is there enough room in the storeroom for all the items?
ANSWER: Multiple Choice (Type 1)
A: Yes
B: No
Answer: B
Workings:
The left hand rectangle can be calculated using:
Area = 15\times 45 = 675 cm^2
The central trapezium can be calculated using:
Area = \dfrac{1}{2}\times (10+45)\times 70 = 1925 cm^2
The right hand rectangle can be calculated using:
Area = 10\times 15 = 150 cm^2
Summing the areas together gives:
Total Area = 675 + 1925 + 150 = 2750 cm^2
The total area required by the boxes is 14 \times 200 cm^2 = 2800 cm^2
2800 > 2750 so the boxes won’t fit in the storeroom.
Marks = 3
Question 3
Which of these two shapes have the same area?
ANSWER: Multiple Choice (Type 1)
A: A & B
B: B & C
C: C & D
D: D & A
Answer: B
Workings:
Area of circle = \pi \times 3^2 = 28.27 cm^2
Area of Parallelogram = 9\times 3 = 27 cm^2
Area of Trapezium = \dfrac{1}{2}\times (6+12)\times 3 = 27 cm^2
Area of Irregular Hexagon = 5\times 3 + 4\times 2 = 23 cm^2
So the Parallelogram (B) and Trapezium (C) both have the same area.
Marks = 2
Question 4
A gardener is planning a new garden that is in the shape of a parallelogram. It features two ponds and a flower bed.
The rest of the space will be filled with grass.
The plan of the garden has been drawn to scale on a 1 cm grid labelled below.
1 cm = 5 m
Calculate the area that will be covered with grass.
Give your answer to 2 decimal places in m^2.
ANSWER: Simple Text Answer
Answer: 885.84
Workings:
Calculating the total area of the Parallelogram gives:
Area = 30\times 50 = 1500 m^2
Calculate Flower Bed as area of a trapezium:
Area = \dfrac{1}{2}\times(15+5)\times 30 = 300 m^2
The ponds are semi-circles with the same area so together make one circle. Calculating its area gives:
Area = \pi\times 10^2 = 314.159 m^2
Subtracting the area of the flower bed and ponds from the total are gives:
1500-300-314.159 = 885.84 m^2
Marks = 3
Question 5
In the diagram the combined area of triangles ACB and FDE are equal to the area of the parallelogram BCDF.
CD = x\\ DE = xFE = 2 cm
Find the value of x.
ANSWER: Simple Text Answer
Answer: 2
Workings:
We can write this as an equation:
x^2 = 2\times \dfrac{1}{2}\times 2\times x = 2x
Rearranging gives x^2-2x = 0
x(x-2) = 0So x = 0 OR x = 2
Therefore x = 2
Marks = 3
Question 6
The diagram shows a regular hexagon set inside a trapezium.
Find the area of the regular hexagon BGHFEC.
Give your answer to 2 decimal places in cm^2.
ANSWER: Simple Text Answer
Answer: 93.53
Workings:
We can find the side length of an equilateral triangle with:
\dfrac{18}{3} = 6 cm
Calculate the height of an equilateral triangle using:
\sqrt{6^2-3^2} = 3\sqrt{3}
Area of triangle is given by:
\dfrac{1}{2}\times 6 \times 3\sqrt{3} = 9\sqrt{3}
Hexagon consists of 6 triangles, so total area of it can be found using:
6\times 9\sqrt{3} = 54\sqrt{3} = 93.53 cm^2
Marks = 3
Question 7
The diagram shows a regular hexagon set inside an isosceles trapezium.
BG = 4 cm
Find the exact total area of the shaded triangles ACE and FHI.
ANSWER: Multiple Choice (Type 1)
A: 7\sqrt{3}
B: 8\sqrt{3}
C: 9\sqrt{3}
D: 10\sqrt{3}
Answer: B
Workings:
The height of a triangle can be found using:
\sqrt{4^2-2^2} = \sqrt{12} = 2\sqrt{3}
Therefore the area of a triangle can be calculated using:
\dfrac{1}{2}\times 4\times 2\sqrt{3} = 4\sqrt{3}
We need the area of two triangles, so
2\times 4\sqrt{3} = 8\sqrt{3} cm^2 gives us the total area.
Marks = 3