A. 48√3 \({cm}^{2}\)
B. 128 √3\({cm}^{2}\)
C. 9.6 √3\({cm}^{2}\)
D. 64 √3\({cm}^{2}\)

Answer: Option: D

Explanation:
Area of an equilateral triangle = √3/4 \({s}^{2}\)
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 \({cm}^{2}\)

2. If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?

A. 120 c \({m}^{2}\)
B. 130 c \({m}^{2}\)
C. 312 c \({m}^{2}\)
D. 315 c \({M}^{2}\)

Answer: Option: A

Explanation:
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.

Area of the triangle = \(\frac{1}{2}\) * 24 * 10 = 120 c\({m}^{2}\)2

3. The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

A. 25 c \({m}^{2}\)
B. 42 c \({m}^{2}\)
C. 49 c \({m}^{2}\)
D. 35 c \({m}^{2}\)

Answer: Option: D

Explanation:

Area of a triangle = r * s

Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * \(\frac{28}{2}\) = 35 c\({m}^{2}\)

4. Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.

A. 225 c\({m}^{2}\)
B. 275 c\({m}^{2}\)
C. 285 c\({m}^{2}\)
D. 315 c\({m}^{2}\)

Answer: Option: C

Explanation:
Area of a trapezium = \(\frac{1}{2}\) (sum of parallel sides) * (perpendicular distance between them) = \(\frac{1}{2}\) (20 + 18) * (15) = 285 c\({m}^{2}\)

5. Find the area of a parallelogram with base 24 cm and height 16 cm.

A. 262 c\({m}^{2}\)
B. 384 c\({m}^{2}\)
C. 192 c\({m}^{2}\)
D. 131 c\({m}^{2}\)

Answer: Option: B

Explanation:
Area of a parallelogram = base * height = 24 * 16 = 384 c\({m}^{2}\)

A. 1 : 96
B. 1 : 48
C. 1 : 84
D. 1 : 68

Answer: Option: C

Explanation:
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.

(4x)(3x) = 6912
12\({X}^{2}\) = 6912
\({X}^{2}\) = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12\({X}^{2}\) = 1 : 4x = 1: 96.

2. The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?

A. 8.5 m
B. 17 m
C. 34 m
D. 51 m

Answer: Option: B

Explanation:
Let the breadth of the plot be b m.

Length of the plot = 3 b m
(3b)(b) = 867
3\({b}^{2}\) = 867
b2 = 289 = 172 (b > 0)
b = 17 m.

3. The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?

A. 27 m
B. 24 m
C. 18 m
D. 21 m

Answer: Option: C

Explanation:
Let the length and the breadth of the floor be l m and b m respectively.

l = b + 200% of b = l + 2b = 3b
Area of the floor = \(\frac{324}{3}\) = 108 sq m
l b = 108 i.e., l * \(\frac{I}{2}\) = 108
\(\frac{I}{2}\) = 324 => l = 18.

4. An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

A. Rs. 3642.40
B. Rs. 3868.80
C. Rs. 4216.20
D. Rs. 4082.40

Answer: Option: D

Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + \(\frac{40}{100}\) ) 6 (1 + \(\frac{25}{100}\) )
= 51.84(1.4)(\(\frac{5}{4}\) ) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 – 0.04) = 4095 – 12.6 = Rs. 4082.40

5. What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?

A. Rs. 3944
B. Rs. 3828
C. Rs. 4176
D. Rs. 4176

Answer: Option: A

Explanation:
Let the side of the square plot be a ft.

\({a}^{2}\)= 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.

A. 600 cm
B. 800 cm
C. 400 cm
D. 1000 cm

Answer: Option: B

Explanation:
Area of the square = s * s = 5(125 * 64)

=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm

2. A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?

A. 60 c\({m}^{2}\)
B. 30 c\({m}^{2}\)
C. 45 c\({m}^{2}\)
D. 15 c\({m}^{2}\)

Answer: Option: B

Explanation:
The circumference of the circle is equal to the permeter of the rectangle.

Let l = 6x and b = 5x 2(6x + 5x) = 2 * \(\frac{22}{7}\) * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 c\({m}^{2}\)

3. The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.

A. 18 : 5
B. 7 : 16
C. 5 : 14
D. 5 : 16

Answer: Option: D

Explanation:
Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.

\({a}^{2}\) = 4096 = 212
a = \({212}^{1/2}\) = 26 = 64
L = 2a and b = a – 24
b : l = a – 24 : 2a = 40 : 128 = 5 : 16

4. The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.

A. 200 sq cm
B. 72 sq cm
C. 162 sq cm
D. Cannot be determined

Answer: Option: D

Explanation:
Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.

4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
The area of the square cannot be found.

5. The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)

A. 77.14 cm
B. 47.14 cm
C. 84.92 cm
D. 23.57 cm

Answer: Option: D

Explanation:
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= \(\frac{1}{2}\)(∏)(15)
= \(\frac{1}{2}\)(\(\frac{22}{7}\))(15) = \(\frac{330}{14}\) = 23.57 cm to two decimal places