### Length, Perimeter and Area

Worked Exercise

- 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?
- 85
- 30
- 20
- 30.10

Working

1 M = 100cm

8½m = ?

8½ x 100 = 850cm

1 piece = 28 cm

? = 850cm

=^{850}/_{28}= 30 complete pieces remainder 10cm

- The figure below represents a flower garden

What is the perimeter of the garden?- 25m
- 38.5m
- 11m
- 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)

- 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?
- 224
- 112
- 108
- 84

Working

Area of a trapezium = ½h (a + b)

= ½ x 8 x (10+18)

= ½ x 8 x 28

= 112cm²

- The figure below shows vegetable garden.

What is the perimeter?- 0.526m
- 5.26m
- 52.6m
- 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

The correct answer is (52.6)

- What is the perimeter of the following shape?
- 88cm
- 44cm
- 176cm
- 56cm

Working

P = circumference of a circle of radius 7cm

= 2Π r

= 2 x^{22}/_{7}x 7

= (44 cm)

- 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?- 18
- 67.5
- 27
- 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)

- 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?
- 25cm
- 24cm
- 19cm
- 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)

- What is the surface area of an open cylinder whose radius is 6.3cm and height of 25cm.
- 114.74cm²
- 1239.48cm²
- 3118.50cm²
- 619cm²

Working

Total surface area = Πr^{2}+Πdh

= (^{22}/_{7}x 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)

- A Welder made a door with a design as shown below.

What is its area? (Take Π =^{22}/_{7})- 15.12m²
- 12.04m²
- 13.36m²
- 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)

- 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})- 12
- 17
- 18
- 19

Working

Perimeter =½ П d + d

= (½ x^{22}/_{7 }x 28 + 28)

= 72

No of posts =^{Perimeter}/_{Interval}

=^{72}/_{4}= 18 posts

The correct answer is C (18)

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