Mathematics - Herons Formula
Exam Duration: 45 Mins Total Questions : 30
The perimeter of a triangular field is 144 m and the ratio of its sides is 3: 4: 5. Find the area of the field.
- (a)
864 sq.m
- (b)
764 sq.m
- (c)
854 sq.m
- (d)
754 sq.m
The edges of a triangular board are 6 cm, 8 cm and 10 cm. What is the cost of painting it at the rate of 9 paise per cm2?
- (a)
Rs 2.00
- (b)
Rs 2.16
- (c)
Rs 2.48
- (d)
Rs 3.00
What is the area of a triangle whose sides are 13 cm, 14 cm and 15 cm?
- (a)
84 sq.cm
- (b)
64 sq.cm
- (c)
82 sq.cm
- (d)
48 sq.cm
Two adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of its diagonals is 6.5 cm. Find the area of parallelogram.
- (a)
\(5\sqrt 3\ cm^2\)
- (b)
\(10\sqrt 3\ cm^2\)
- (c)
\(15\sqrt 3\ cm^2\)
- (d)
\(20\sqrt 3\ cm^2\)
The sides of a triangle are in the ratio of 13: 14: 15 and its perimeter is 84 cm. Determine the area of the triangle.
- (a)
136 cm2
- (b)
236 cm2
- (c)
336 cm2
- (d)
436 cm2
The adjacent sides of a parallelogram are 4 cm and 9 cm. What is the ratio of its altitudes?
- (a)
16: 81
- (b)
9: 4
- (c)
2: 3
- (d)
3: 2
The perimeter of a rhombus is 52 cm and one of its diagonals is 24 cm. Determine the length of the other diagonal.
- (a)
24 cm
- (b)
10 cm
- (c)
\(2\frac{1}{6} \ cm\)
- (d)
12 cm
The area of a rhombus is 28 cm2 and one of its diagonals is 4 cm. What is its perimeter?
- (a)
\(4\sqrt 53\ cm\)
- (b)
36 cm
- (c)
\(2\sqrt 53\ cm\)
- (d)
52 cm
In \(\triangle\) ABC,AB = 6 cm, BC= 7 cm and AC = 5 cm. What is the area of \(\triangle\) ABC?
- (a)
\(6\sqrt 6\ cm^2\)
- (b)
\(6\sqrt 3\ cm^2\)
- (c)
\(6\sqrt 2\ cm^2\)
- (d)
\(9\sqrt 6\ cm^2\)
If the angles of a triangle are in the ratio 5 : 3: 7, what is such a triangle called?
- (a)
An acute-angled triangle
- (b)
An obtuse-angled triangle
- (c)
A right triangle
- (d)
An isosceles triangle
The base of an isosceles right triangle is 30 cm. Find its area.
- (a)
225 cm2
- (b)
\(225\sqrt 3\ cm^2\)
- (c)
\(225\sqrt 2\ cm^2\)
- (d)
450 cm2
White and grey coloured triangular plastic sheets are used to make a toy as shown in figure. Find the difference in areas of shaded and unshaded coloured sheets used for making the toy.
- (a)
1 cm2
- (b)
0 cm2
- (c)
\(5\sqrt 2\ cm^2\)
- (d)
\(16\sqrt 2\ cm^2\)
If the area of an isosceles right triangle is 8 cm2, what is its perimeter?
- (a)
\((8+\sqrt 2)\ cm\)
- (b)
\((8+4\sqrt 2)\ cm\)
- (c)
\((4+8\sqrt 2)\ cm\)
- (d)
\(12\sqrt 2\ cm\)
The perimeter of an equilateral triangle is 60 m. What is its area?
- (a)
\(10\sqrt 3\ m^2\)
- (b)
\(15\sqrt 3\ m^2\)
- (c)
\(20\sqrt 3\ m^2\)
- (d)
\(100\sqrt 3\ m^2\)
If the area of an equilateral triangle is \(16\sqrt 3\ cm^2\), what is the perimeter of the triangle?
- (a)
48 cm
- (b)
24 cm
- (c)
12 cm
- (d)
306 cm
Which of the following should we have in order to find the area of a triangle by Heron's formula?
- (a)
All the angles
- (b)
Altitudes
- (c)
Two sides and the including angle
- (d)
All the sides
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 15 cm, 14 cm and 13 cm and the parallelogram stands on the side of 15 cm, find the height of the parallelogram.
- (a)
4.2 cm
- (b)
5.6 cm
- (c)
8.4 cm
- (d)
2.1 cm
What is the length of each side of an equilateral triangle having an area of \(9\sqrt 3\ cm^2\)?
- (a)
8 cm
- (b)
36 cm
- (c)
4 cm
- (d)
6 cm
A triangular park in a city has dimensions 10 m x 90 m x 110 m. A contract is given to a company for planting grass in the park at the rate of Rs 4000 per hectare. What is the amount to be paid to the company?(Take \(\sqrt 2=1.414\ \) and One hectare = 10000 m2)
- (a)
Rs 1968.60
- (b)
Rs 1698.60
- (c)
Rs 1986.60
- (d)
Rs 1696.80
Area of a given triangle is x1 square units. If the sides of this triangle are doubled, the area of the new triangle becomes x2 square units. Calculate the percentage increase in the area.
- (a)
100 %
- (b)
200 %
- (c)
300 %
- (d)
400 %
In a quadrilateral ABCD if AB = 5 m, BC= 5 m,CD = 6m, AD = 6m and diagonal AC = 6 m, what is its area?
- (a)
\(2(4+3\sqrt 3)\ m^2\)
- (b)
\(3(4+3\sqrt 3)\ m^2\)
- (c)
\(5(4+3\sqrt 3)\ m^2\)
- (d)
\(7(4+3\sqrt 3)\ m^2\)
In a quadrilateral ABCD if AB = 9 m, BC = 40 m, CD = 28 m, AD = 15 m and \(\angle ABC=90^0\),find its area.
- (a)
136 m2
- (b)
163 m2
- (c)
360 m2
- (d)
306 m2
In the given figure, the area of the \(\Delta\)ABC is
- (a)
13.24 cm2
- (b)
12.28 cm2
- (c)
11.32 cm2
- (d)
15.37 cm2
The perimeter of a triangle is 540 m and its sides are in the ratio 25 : 17 : 12. Find its area.
- (a)
9100 m2
- (b)
9000 m2
- (c)
9200 m2
- (d)
9500 m2
The area of a parallelogram ABCD in which AB = 12 cm, BC = 9 cm and diagonal AC = 15 cm is k cm2. Find the value of \(\frac{K-100}{4}\)
- (a)
3
- (b)
4
- (c)
2
- (d)
5
A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. 5 per cm2. Find the cost of painting.
- (a)
Rs.880
- (b)
Rs.1020
- (c)
Rs.960
- (d)
Rs.980
The area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm is K\(\sqrt{30}\) cm2. Find the value of k.
- (a)
8
- (b)
6
- (c)
7
- (d)
9
A field is in the shape of a trapezium whose parallel sides are 25 m and 10m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
- (a)
196 cm2
- (b)
186 cm2
- (c)
169 cm2
- (d)
199 cm2
Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs. 7 per m2.
- (a)
Rs.9500
- (b)
Rs.11000
- (c)
Rs.10500
- (d)
Rs.12500
Find the area of quadrilateral ABCD in which AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and \(\angle\)ABC = 90°.
- (a)
300 cm2
- (b)
180 cm2
- (c)
126 cm2
- (d)
306 cm2