Test Preparation on Mensuration For Competitive Exam

1.

What is the area of an equilateral triangle of side 16 cm?

Area of an equilateral triangle = √3/4 S2 If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;

2.

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

The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm. Area of the triangle = 1/2 * 24 * 10 = 120 cm2

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?

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 * 28/2 = 35 cm2

4.

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

Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2

5.

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

Area of a parallelogram = base * height = 24 * 16 = 384 cm2

6.

The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?

Let the length and the breadth of the rectangle be 4x cm and 3x respectively. (4x)(3x) = 6912 12x2 = 6912 x2 = 576 = 4 * 144 = 22 * 122 (x > 0) => x = 2 * 12 = 24 Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.

7.

The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?

Let the sides of the rectangle be l and b respectively. From the given data, (?l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m.

8.

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?

Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m.

9.

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?

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 = 324/3 = 108 sq m l b = 108 i.e., l * l/3 = 108 l2 = 324 => l = 18.

10.

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?

Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(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


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