Wednesday, 15 September 2021 06:19

# Measurements - Class 8 Mathematics Revision Notes

### Length, Perimeter and Area

Worked Exercise

1. Tracy used a piece of wire m long to support tomato plants in the garden. The wire was cut into pieces of 28cm long. How many complete pieces were obtained?
1. 85
2. 30
3. 20
4. 30.10
Working
1 M = 100cm
8½m = ?
8½ x 100 = 850cm
1 piece = 28 cm
? = 850cm
= 850/28
= 30 complete pieces remainder 10cm
2. The figure below represents a flower garden

What is the perimeter of the garden?
1. 25m
2. 38.5m
3. 11m
4. 44m
Working
P = ¼П d + r + r
= ( ¼ x 22/7 x 14) + (7+7)
= 11 + 14
= 25 m
The correct answer is A (25)
3. The parallel sides of a trapezium measure 10cm by 18cm respectively. If the distance between the parallel sides is 8cm, what is the area of the trapezium in cm²?
1. 224
2. 112
3. 108
4. 84
Working
Area of a trapezium = ½h (a + b)
= ½ x 8 x (10+18)
= ½ x 8 x 28
= 112cm²
4. The figure below shows vegetable garden.

What is the perimeter?
1. 0.526m
2. 5.26m
3. 52.6m
4. 526m
Working
Perimeter of semi-circle
= ½П d(Circumference only)
=½ x 2 x 22/7 x 7
= 22m
To get DC = √ 25 – √ 16
= √ 9
= 3m
Length DE = AB – ED
= 12.8 – 7
= 5.8m
Total length 12.8+ 5 + 3 + 5.8 + 22 + 4
= 52.6 m
5. What is the perimeter of the following shape?

1. 88cm
2. 44cm
3. 176cm
4. 56cm
Working
P = circumference of a circle of radius 7cm
= 2Π r
= 2 x 22/7 x 7
= (44 cm)
6. The figure below shows a right angled triangle LMN in which LM = 7.5cm and LN = 19.5cm

What is the area of the triangle in cm²?
1. 18
2. 67.5
3. 27
4. 34.5
Working
Apply Pythagoras relation in triangle LMN
LN² = LM² + NM²
Nm² = LN² – LN²
= 19.5² – 7.5²
= 380.25 – 56.25
= 324
NM = √ 324
= 18 cm
Area of triangle LMN
= Base x height
= ½ X 18 X 7.5
= 67.5cm²
The correct answer is B (67.5cm²)
7. The area of a right-angled triangle is 84cm². If the height of the triangle is 7cm, what is the length of the longest side?
1. 25cm
2. 24cm
3. 19cm
4. 12cm
Working

The Pythagoras relationship states that
H² = b² + h²
But Area = ½bh
84 =½ x b x 7
84 x 2 = 7b
24 = b
H² = 24² + 7²
H² = 576 + 49
H² = 625
H = 25
Therefore the correct answer is 25cm (A)
8. What is the surface area of an open cylinder whose radius is 6.3cm and height of 25cm.
1. 114.74cm²
2. 1239.48cm²
3. 3118.50cm²
4. 619cm²
Working
Total surface area = Πr2+Πdh
= ( 22/7x 6.3 x 6.3) + 2 x 22/7 x 6.3 x 25
= 124.74 + 990
= 1114.74 cm²
The correct answer is 1114.74 cm² (A)
9. A Welder made a door with a design as shown below.

What is its area? (Take Π =22/7 )
1. 15.12m²
2. 12.04m²
3. 13.36m²
4. 21.28m²
Working
Area of the semi- circle = ½Π r²
= ½ x 22/7 x 1.4 x 1.4
= 3.08m²
Area of the rectangle = L x w
= 3.2 x 2.8
= 8.96 m²
Total area = (3.08 + 8.96 )m²
= 12.04 m²
The correct answer is B (12.04m²)
10. The diagram below represents a plot with a diameter of 28 meters.

The plot was fenced by erecting posts 4m apart. How many posts were used ? (Π = 22/7)
1. 12
2. 17
3. 18
4. 19
Working
Perimeter =½ П d + d
= (½ x 22/x 28 + 28)
= 72
No of posts = Perimeter/Interval
=72/4
= 18 posts
The correct answer is C (18)