Area Questions and Answers

Q: Original breadth of a rectangular box is 20 cm. The box was then remade in such a way that its length got increased by 30% but the breadth decreased by 20%. This led to an increase in area by 100sq.cm. What is the new area of the box?

Let the original length be \( L \), with breadth 20 cm.\[ A_{\text{old}} = 20L \]The length rises by 30% and the breadth falls by 20%:\[ A_{\text{new}} = (1.3L)(0.8 \times 20) = (1.3L)(16) = 20.8L \]\[ A_{\text{new}} - A_{\text{old}} = 0.8L = 100 \quad\Longrightarrow\quad L = 125 \text{ cm} \]\[ A_{\text{new}} = 20.8 \times 125 = 2600 \text{ cm}^{2} \]The question asks for the new area; the old one is 2500 cm², offered as the last distractor.

Q: A rectangular margin has a length of 48 cm and an area of 840 sq. cm. Its area becomes \( 2\tfrac{6}{7} \) times the original when the breadth alone is increased. What is the perimeter of the enlarged rectangle?

Find the original breadth, then the new one.\[ b = \frac{840}{48} = 17.5 \text{ cm} \]\[ A_{\text{new}} = 840 \times 2\tfrac{6}{7} = 840 \times \frac{20}{7} = 2400 \text{ cm}^{2} \]The length is unchanged, so\[ b_{\text{new}} = \frac{2400}{48} = 50 \text{ cm} \]\[ \text{perimeter} = 2(48 + 50) = 196 \text{ cm} = 1.96 \text{ m} \]The answer is offered in metres, so the 196 cm must be divided by 100 - the step the distractors are spaced around.

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121.

Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?

A.425
B.476
C.450
D.350

Answer: B

The 0.25 m border runs along all four sides, so each dimension loses twice that.

\[ \text{tiled area} = (4 - 0.5)(9 - 0.5) = 3.5 \times 8.5 = 29.75 \text{ m}^{2} \]

\[ \text{tile} = 0.25 \times 0.25 = 0.0625 \text{ m}^{2} \]

\[ n = \frac{29.75}{0.0625} = 476 \]

Subtracting only 0.25 m from each dimension instead of 0.5 is the usual slip - the space is left on both opposite sides.

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122.

If the area of circle is 616 sq cm then its circumference?

A.78 m
B.88 m
C.75 m
D.70 m

Answer: B

Find the radius from the area, then use it for the circumference.

\[ \pi r^{2} = 616 \quad\Longrightarrow\quad r^{2} = \frac{616 \times 7}{22} = 196 \]

\[ r = 14 \text{ cm} \]

\[ C = 2\pi r = 2 \times \frac{22}{7} \times 14 = 88 \text{ cm} \]

The two formulas share \( \pi \) but not the power of \( r \), so the radius must be extracted before the circumference can be found.

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123.

What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Rs. 10 per square meter ?

A.3410
B.3420
C.3430
D.3440

Answer: D

We know Perimeter = 2(l+b), right
So,
2(l+b) = 340
As we have to make 1 meter boundary around this, so
Area of boundary = ((l+2)+(b+2)-lb)
= 2(l+b)+4 = 340+4 = 344
So required cost will be = 344 * 10 = 3440

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124.

Original breadth of a rectangular box is 20 cm. The box was then remade in such a way that its length got increased by 30% but the breadth decreased by 20%. This led to an increase in area by 100sq.cm. What is the new area of the box?

A.3600 sq.cm.
B.3200 sq.cm.
C.2600 sq.cm.
D.2500 sq.cm.

Answer: C

Let the original length be \( L \), with breadth 20 cm.

\[ A_{\text{old}} = 20L \]

The length rises by 30% and the breadth falls by 20%:

\[ A_{\text{new}} = (1.3L)(0.8 \times 20) = (1.3L)(16) = 20.8L \]

\[ A_{\text{new}} - A_{\text{old}} = 0.8L = 100 \quad\Longrightarrow\quad L = 125 \text{ cm} \]

\[ A_{\text{new}} = 20.8 \times 125 = 2600 \text{ cm}^{2} \]

The question asks for the new area; the old one is 2500 cm², offered as the last distractor.

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125.

A rectangular margin has a length of 48 cm and an area of 840 sq. cm. Its area becomes \( 2\tfrac{6}{7} \) times the original when the breadth alone is increased. What is the perimeter of the enlarged rectangle?

A.1.69 m
B.1.85 m
C.1.96 m
D.2.25 m

Answer: C

Find the original breadth, then the new one.

\[ b = \frac{840}{48} = 17.5 \text{ cm} \]

\[ A_{\text{new}} = 840 \times 2\tfrac{6}{7} = 840 \times \frac{20}{7} = 2400 \text{ cm}^{2} \]

The length is unchanged, so

\[ b_{\text{new}} = \frac{2400}{48} = 50 \text{ cm} \]

\[ \text{perimeter} = 2(48 + 50) = 196 \text{ cm} = 1.96 \text{ m} \]

The answer is offered in metres, so the 196 cm must be divided by 100 - the step the distractors are spaced around.

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126.

The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?

A.432 sq m
B.356 sq m
C.452 sq m
D.428 sq m

Answer: A

\[ l = 3b \quad\Longrightarrow\quad 2(3b + b) = 96 \quad\Longrightarrow\quad 8b = 96 \]

\[ b = 12 \text{ m}, \qquad l = 36 \text{ m} \]

\[ A = 36 \times 12 = 432 \text{ m}^{2} \]

The perimeter contains four "breadths" worth of length in total (\( 2 \times 3b + 2 \times b \)), which is what makes the division by 8 so clean.

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