Area and Perimeter: Every Shape (Complete Guide) — Worksheet & Memo

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Grade 8 · Measurement

Area and Perimeter: Every Shape (Complete Guide)

MARKING GUIDELINE

Marks

Duration

1 hour

Questions

Name:

Class:

Date:

Mark

/ 38

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 rectangle 8 cm by 5 cm is …
(1)
A)26 cm²
B)40 cm²✓
C)13 cm²
D)80 cm²
Answer: B — A = l × b.
- A — that is the PERIMETER
- C — added the two sides
- D — doubled the area
1.2
The perimeter of that same rectangle is …
(1)
A)40 cm
B)26 cm✓
C)13 cm
D)80 cm
Answer: B — P = 2(8 + 5).
- A — that is the AREA
- C — added the two sides only once
- D — doubled the area
1.3
The area of a triangle with base 10 cm and PERPENDICULAR height 6 cm is …
(1)
A)60 cm²
B)30 cm²✓
C)16 cm²
D)32 cm²
Answer: B — A = ½ × b × h.
- A — forgot to halve
- C — added base and height
- D — that is the perimeter of something else
1.4
The height used in the area of a triangle must be …
(1)
A)the longest side
B)PERPENDICULAR to the base✓
C)the shortest side
D)any side
Answer: B — A slanted side is longer and would give too big an area.
- A — the longest side is usually slanted
- C — not necessarily
- D — only the perpendicular height works
1.5
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)22 cm
Answer: B — C = 2πr = 2 × 3,14 × 7.
- A — that is the AREA formula, πr²
- C — used πr instead of 2πr
- D — rounded from the wrong formula
1.6
The AREA of that same circle is …
(1)
A)43,96 cm²
B)153,86 cm²✓
C)21,98 cm²
D)307,72 cm²
Answer: B — A = πr² = 3,14 × 49.
- A — that is the CIRCUMFERENCE
- C — used πr
- D — used 2πr²
1.7
A circle has a diameter of 10 cm. Its area, with π ≈ 3,14, is …
(1)
A)314 cm²
B)78,5 cm²✓
C)31,4 cm²
D)157 cm²
Answer: B — The radius is 5, so A = 3,14 × 25.
- A — used the DIAMETER as the radius
- C — that is the circumference
- D — used 2πr²
1.8
The area of a square is 49 cm². Its perimeter is …
(1)
A)7 cm
B)28 cm✓
C)196 cm
D)14 cm
Answer: B — Side = 7 cm, so P = 4 × 7.
- A — that is the SIDE
- C — multiplied the area by 4
- D — used two sides only
1.9
A rectangle has an area of 48 cm² and a length of 8 cm. Its breadth is …
(1)
A)40 cm
B)6 cm✓
C)56 cm
D)24 cm
Answer: B — 48 ÷ 8 = 6 cm.
- A — subtracted instead of dividing
- C — added instead of dividing
- D — halved the area
1.10
If the sides of a square are DOUBLED, its area is multiplied by …
(1)
A)2
B)4✓
C)8
D)16
Answer: B — Area scales by the square of the length factor.
- A — that is the LENGTH factor
- C — that is the volume factor
- D — that would be a factor of 4 on the sides

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

[12 MARKS]

The diagram below shows a rectangle. Use π ≈ 3,14 where needed.

2.1
Calculate the perimeter of the rectangle.
(3)
P = 2(l + b) = 2(8 + 5) (2)
= 26 cm (1)
2.2
Calculate the area of the rectangle, and hence the area of a rectangle whose length and breadth are BOTH doubled.
(3)
A = l × b = 8 × 5 = 40 cm² (2)
Doubling both dimensions multiplies the area by 2 × 2 = 4, so it becomes 160 cm² (1)
2.3
A square has a side of 6 cm. Calculate its perimeter and its area.
(3)
P = 4 × 6 = 24 cm (1)
A = 6 × 6 (1) = 36 cm² (1)
2.4
A different rectangle has an area of 48 cm² and a length of 8 cm. Calculate its breadth.
(3)
A = l × b, so b = A ÷ l (1)
= 48 ÷ 8 (1) = 6 cm (1)

Question 3

[8 MARKS]

The diagram below shows a triangle with its perpendicular height marked.

3.1
Write down the formula for the area of a triangle, and explain where the ½ in it comes from.
(3)
A = 12 × b × h (1)
A triangle is exactly HALF of a rectangle with the same base and the same height (1)
so its area is half of b × h (1)
3.2
Calculate the area of the triangle.
(3)
A = 12 × 10 × 6 (2)
= 30 cm² (1)
3.3
Explain why the height used must be PERPENDICULAR to the base.
(2)
The height must be the shortest distance from the base to the opposite vertex (1); a slanted side is longer and would give too big an area (1)

Question 4

[8 MARKS]

The diagram below shows a circle. Use π ≈ 3,14.

4.1
Calculate the circumference of the circle.
(3)
C = 2πr = 2 × 3,14 × 5 (2)
= 31,4 cm (1)
4.2
A different circle has a radius of 10 cm. Calculate its area.
(3)
A = πr² = 3,14 × 10² (2)
= 314 cm² (1)
4.3
State the difference between the circumference and the area of a circle, and give the unit of each.
(2)
The circumference is the distance round the circle, measured in cm (1); the area is the space inside it, measured in cm² (1)

TOTAL: 38 marks

This question paper consists of 4 questions.