Area of Polygons

14 Grade 10 Essential Mathematics questions on Area of Polygons, with worked marking schemes. 14 questions are available on this topic in full.

Question 1
5 marks
A road sign is in the shape of a rhombus whose diagonals measure 1.2 m and 0.9 m.
(a) Calculate the area of one face of the sign.
(b) Both faces of the sign are painted at a cost of KSh 350 per square metre. Calculate the total cost of painting one sign.
(5 marks)
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Question 2
1 mark
A parallelogram-shaped plot of land in Nyeri has a base of 12 m and a sloping side of 8 m. The perpendicular distance between the base and the side opposite to it is 6 m. What is the area of the plot?
A. 48 m²
B. 96 m²
C. 72 m²
D. 36 m²
(1 mark)
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Question 3
6 marks
A piece of land is made up of a rectangle measuring 20 m by 14 m, with a triangular extension joined along one 14 m end. The triangle has a base of 14 m and a perpendicular height of 6 m.
(a) Calculate the total area of the land.
(b) The owner spreads manure over the whole piece of land at the rate of 2 kg per square metre. Calculate the mass of manure required.
(6 marks)
Marking scheme
(a) Area of rectangle = $20 \times 14 = 280 m^{2}$ (1); area of triangle = $\frac{1}{2}$ × base × height used (1); = $\frac{1}{2}$ × $14 \times 6 = 42 m^{2}$ (1); total area = $280 + 42 = 322 m^{2}$ (1). (b) Mass = $322 \times 2$ (1); = 644 kg (1).
Question 4
4 marks
The floor of a school poultry unit is a rectangle 9 m long and 6 m wide. A concrete feeding platform measuring 3 m by 2 m is built in one corner of this floor.
(a) Calculate the floor area that is left uncovered.
(b) Suggest one reason why the caretaker needs to know this uncovered area.
(4 marks)
Marking scheme
(a) Area of whole floor = $9 \times 6 = 54 m^{2}$ (1); area of platform = $3 \times 2 = 6 m^{2}$ (1); uncovered area = $54 - 6 = 48 m^{2}$ (1). (b) Any one sensible reason, e.g. to work out how much wood shavings/litter to buy, or to decide how many birds the space can hold (1).
Question 5
1 mark
A trapezium-shaped stage has parallel sides measuring 14 m and 10 m, and its area is 96 m². What is the perpendicular distance between the two parallel sides?
A. 4 m
B. 16 m
C. 12 m
D. 8 m
(1 mark)
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Question 6
4 marks
The lid of a cattle feed trough is a regular hexagon of side 30 cm. The perpendicular distance from the centre of the hexagon to the middle of any side is 26 cm. Describe how you would use triangles to find the area of the lid, and calculate that area.
(4 marks)
Marking scheme
Join the centre to each vertex to divide the hexagon into 6 congruent triangles (1); each triangle has base 30 cm and perpendicular height 26 cm (1); area of one triangle = $\frac{1}{2}$ × $30 \times 26 = 390$ cm² (1); area of $l i d = 6 \times 390 = 2340$ cm² (1).
Question 7
1 mark
The floor of a rectangular dining hall measures 12 m by 9 m. It is to be covered completely with square tiles of side 30 cm. How many tiles are needed?
A. 120
B. 360
C. 12 000
D. 1 200
(1 mark)
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Question 8
2 marks
Distinguish between the perpendicular height and the slant side of a parallelogram as used in finding its area.
(2 marks)
Marking scheme
Perpendicular height is the shortest distance between the two parallel sides, measured at right angles to the base, and it is the length used in area = base × perpendicular height (1); the slant side is the sloping side joining the two parallel sides, it is longer than the perpendicular height and using it in place of the height gives too large an area (1).
Question 9
3 marks
A school vegetable garden is in the shape of a trapezium whose parallel sides measure 18 m and 12 m. The perpendicular distance between the parallel sides is 9 m. Calculate the area of the garden.
(3 marks)
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Question 10
1 mark
A regular pentagonal signboard has each side measuring 40 cm, and the perpendicular distance from the centre of the board to the middle of any side is 27.5 cm. What is the area of one face of the signboard?
A. 550 cm²
B. 1 100 cm²
C. 5 500 cm²
D. 2 750 cm²
(1 mark)
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Question 11
1 mark
A rectangular plot of land in Kitale measures 80 m by 50 m. What is the area of the plot in hectares?
A. 0.04 ha
B. 40 ha
C. 4 ha
D. 0.4 ha
(1 mark)
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Question 12
3 marks
A triangular vegetable plot has an area of 84 m² and a base of 14 m. Calculate the perpendicular height of the plot.
(3 marks)
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Question 13
1 mark
A kite made by learners during a games day is in the shape of a rhombus whose diagonals measure 16 cm and 12 cm. What is the area of the kite?
A. 40 cm²
B. 48 cm²
C. 96 cm²
D. 192 cm²
(1 mark)
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Question 14
1 mark
A farmer has a square maize plot. He buys the neighbouring land so that each side of the square plot is now twice as long as before. What happens to the area of the plot?
A. It becomes four times as large
B. It becomes eight times as large
C. It becomes sixteen times as large
D. It becomes twice as large
(1 mark)
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More Grade 10 Essential Mathematics topics

Area of Polygons

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14