Area & Perimeter of 2-D Shapes (Grade 9) — Worksheet & Memo

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Grade 9 · Area & Perimeter

Area & Perimeter of 2-D Shapes (Grade 9)

MARKING GUIDELINE

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 33

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
The area of a trapezium with parallel sides 14 cm and 22 cm and height 9 cm is …
(1)
A)324 cm²
B)162 cm²✓
C)126 cm²
D)45 cm²
Answer: B — A = ½(a + b)h = ½(36)(9).
- A — forgot to halve
- C — used only one parallel side
- D — added the three numbers
1.2
The area of a parallelogram with base 12 cm and PERPENDICULAR height 7 cm is …
(1)
A)42 cm²
B)84 cm²✓
C)38 cm²
D)19 cm²
Answer: B — A = b × h — no halving, unlike a triangle.
- A — halved it as if it were a triangle
- C — that is the perimeter of something else
- D — added base and height
1.3
The circumference of a circle of radius 7 cm, with π ≈ 3,14, is …
(1)
A)153,86 cm
B)43,96 cm✓
C)21,98 cm
D)14 cm
Answer: B — C = 2πr.
- A — that is the AREA
- C — used πr instead of 2πr
- D — that is the diameter
1.4
A circle has an area of 153,86 cm² (π ≈ 3,14). Its RADIUS is …
(1)
A)49 cm
B)7 cm✓
C)14 cm
D)24,5 cm
Answer: B — r² = 153,86 ÷ 3,14 = 49, so r = 7.
- A — forgot to take the square root
- C — that is the diameter
- D — halved the area
1.5
If the RADIUS of a circle is doubled, its area is multiplied by …
(1)
A)2
B)4✓
C)8
D)π
Answer: B — Area depends on r².
- A — that is the factor for the CIRCUMFERENCE
- C — that is the volume factor
- D — π is in both, so it cancels
1.6
A composite shape is a rectangle 10 cm by 6 cm with a 4 cm by 3 cm rectangle cut out. Its area is …
(1)
A)72 cm²
B)48 cm²✓
C)60 cm²
D)12 cm²
Answer: B — 60 − 12 = 48.
- A — ADDED the two areas
- C — forgot to subtract the cut-out
- D — that is the cut-out alone
1.7
The perimeter of a semicircle of radius 10 cm (π ≈ 3,14) is …
(1)
A)31,4 cm
B)51,4 cm✓
C)62,8 cm
D)41,4 cm
Answer: B — Half the circumference (31,4) PLUS the diameter (20).
- A — forgot the straight diameter edge
- C — that is the WHOLE circumference
- D — used a radius of 10 instead of a diameter of 20
1.8
Area is measured in …
(1)
A)cm
B)cm²✓
C)cm³
D)no units
Answer: B — Two lengths multiplied give a square unit.
- A — that is a length
- C — that is a volume
- D — every measurement has a unit
1.9
A square and a circle both have a perimeter of 40 cm. Which has the LARGER area?
(1)
A)the square
B)the circle✓
C)they are equal
D)it cannot be decided
Answer: B — Square: side 10, area 100 cm². Circle: r ≈ 6,37, area ≈ 127 cm².
- A — 100 cm² is the smaller of the two
- C — they are not equal
- D — both areas can be calculated
1.10
The area of a rhombus with diagonals 12 cm and 16 cm is …
(1)
A)192 cm²
B)96 cm²✓
C)28 cm²
D)56 cm²
Answer: B — A = ½ × d₁ × d₂.
- A — forgot to halve
- C — added the diagonals
- D — that is the perimeter of something else

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

A rectangular metal plate is 18 cm long and 12 cm wide. A quarter circle of radius 6 cm is cut away from one corner. Use π = 3,14.

2.1
Calculate the area of the whole rectangle.
(3)
A = l × b = 18 × 12 (2)
= 216 cm² (1)
2.2
Calculate the area of the quarter circle that is cut away, correct to two decimal places.
(4)
Full circle = πr² = 3,14 × 6² (1)
= 3,14 × 36 = 113,04 cm² (1)
Quarter = 113,044 (1)
= 28,26 cm² (1)
2.3
Hence calculate the area of the metal that remains.
(3)
216 − 28,26 (2)
= 187,74 cm² (1)

Question 3

[13 MARKS]

Answer the following.

3.1
A trapezium has parallel sides of 14 cm and 22 cm and a perpendicular height of 9 cm. Calculate its area.
(3)
A = ½(a + b)h = ½(14 + 22)(9) (2)
= ½ × 36 × 9 = 162 cm² (1)
3.2
The circumference of a circle is 44 cm. Calculate its radius, correct to two decimal places. Use π = 3,14.
(4)
C = 2πr, so 44 = 2(3,14)r (1)
44 = 6,28r (1)
r = 446,28 (1)
= 7,01 cm (1)
3.3
Hence calculate the area of that circle, correct to one decimal place.
(3)
A = πr² = 3,14 × (7,01)² (2)
= 154,3 cm² (1)
3.4
The radius of a circle is doubled. Explain what happens to its area, and justify your answer.
(3)
The area becomes four times as large (1)
A = πr², and (2r)² = 4r² (2)

TOTAL: 33 marks

This question paper consists of 3 questions.