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