CBSE Class 9 Maths Herons Formula MCQs

Question. In the given figure, the area of the ΔABC is

(A) 13.24 cm²
(B) 12.28 cm²
(C) 11.32 cm²
(D) 15.37 cm²
Answer : B

Question. The difference between the semi-perimeter and the sides of a DABC are 8 cm, 7 cm and 5 cm respectively. The area of the triangle is______.
(A) 20√7 cm²
(B) 10√14 cm²
(C) 20√14 cm²
(D) 140 cm²
Answer : C

Question. If each side of the rhombus is 40 m and its longer diagonal is 48 m, then the area of rhombus is______.
(A) 1536 m²
(B) 1636 m²
(C) 1236 m²
(D) 1336 m²
Answer : A

Question. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
(A) 15 cm
(B) 14 cm
(C) 12 cm
(D) 13 cm
Answer : C

Question. 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 k −100/4.
(A) 3
(B) 4
(C) 2
(D) 5
Answer : C

Question. 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
Answer : B

Question. The perimeter of an isosceles triangle is 32 cm. The ratio of one of the equal sides to its base is 3 : 2. Find the area of the triangle.
(A) 48 cm²
(B) 28√3 cm²
(C) 32√2 cm²
(D) 44 cm²
Answer : C

Question. In the given parallelogram, find the length of the altitude from vertex A on the side DC.

(A) 18 cm
(B) 12 cm
(C) 15 cm
(D) 25 cm
Answer : C

Question. In the given figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram ΔBCE of same area as that of DABC is constructed. Find the height DF of the parallelogram.

(A) 3 cm
(B) 6 cm
(C) 4 cm
(D) 2 cm
Answer : A

Question. The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is______.
(A) 30√7 cm
(B) (15√7/2)cm
(C) (15√7/4) cm
(D) 30 cm
Answer : C

Question. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m.
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
Answer : A

Question. A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of ₹ 5 per cm². Find the cost of painting.
(A) ₹ 880
(B) ₹ 1020
(C) ₹ 960
(D) ₹ 980
Answer : C

Question. The area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm is k √30 cm². Find the value of k.
(A) 8
(B) 6
(C) 7
(D) 9
Answer : A

Question. The base of an isosceles triangle measures 24 cm and its area is 192 cm². Find its perimeter.
(A) 64 cm
(B) 46 cm
(C) 84 cm
(D) 54 cm
Answer : A

Question. The perimeter of a field in the form of an equilateral triangle is 36 cm, then its area is given by
(A) 98√3 cm²
(B) 8√3 cm²
(C) 42√3 cm²
(D) 36√3 cm²
Answer : D

Question. Tanya joined four triangles of cardboard to create a mask of Joker as shown in the given figure. Find the total area of the mask. [Given √2 = 1.41, √3 = 1.73 ]

(A) 59.86 cm²
(B) 50 cm²
(C) 59 cm²
(D) 53 cm²
Answer : A

Question. An umbrella is made by stiching 12 triangular pieces of cloth of two different colours as shown in given figure. Each piece measuring 40 cm, 40 cm and 18 cm. How much cloth of each colour is required for the umbrella?

(A) 2104.56 cm² , 2104.56 cm²
(B) 4209.22 cm² , 2104.56 cm²
(C) 1204.61 cm² , 1204.61 cm²
(D) 2014.61 cm² ,1204.61 cm²
Answer : A

Question. A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown below. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the total area of paper needed to make the hand fan.

(A) 840 cm²
(B) 1680 cm²
(C) 480 cm²
(D) 7844 cm²
Answer : B

Question. Right isosceles triangles are constructed on the sides of right angled ΔABC with sides 3, 4, 5 units, as shown. A capital letter indicates area of each triangle. Which one of the following is true?

(A) X + Z = Y + W
(B) W + X = Z
(C) Y + Z = X
(D) X + W = 1/2 (Y + Z)
Answer : C

Question. State 'T' for true and 'F' for false.
(I) The lengths of the three sides of a triangular field are 40 m, 24 m and 32 m respectively. The area of the triangle is 384 m².
(II) The area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm is 18 cm².
(III) An advertisement board is in the form of an isosceles triangle with its sides equal to 12 m, 10 m and 10 m. The cost of painting it at ₹ 2.25 per m2 is ₹ 112.
(IV) Heron's formula cannot be used to calculate area of quadrilaterals.
     (I)     (II)     (III)    (IV)
(A) T       F       F        T
(B) F       T       F        F
(C) T       F       T        F
(D) T       F       F        F
Answer : D

Question. Suman made a picture with some white paper and a single coloured paper as shown in figure. White paper is available at her home and free of cost. The cost of coloured paper used is at the rate of 10p per cm². 
Find the total cost of the coloured paper used. (Take √3 = 1.732 and √11 = 3.31)

(A) ₹ 14.92
(B) ₹ 14
(C) ₹ 16
(D) ₹ 13
Answer : A

Question. Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of ₹ 7 per m².
(A) ₹ 9500
(B) ₹ 11000
(C) ₹ 10500
(D) ₹ 12500
Answer : C

Question. ABC is an equilateral triangle of side 4√3 cm. P, Q and R are mid-points of AB, CA and BC respectively. Find the area of triangle PQR is ______.
(A) 3√3 cm²
(B) 2√3 cm²
(C) (√3/2)cm²
(D) (√3/4)cm²
Answer : A

Question. A design is made on a rectangular tile of dimensions 50 cm × 70 cm as shown in figure. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile respectively.

(A) 1632 cm², 1886 cm²
(B) 1538 cm², 1632 cm²
(C) 1632 cm², 1868 cm²
(D) 1538 cm², 1632 cm²
Answer : C

Question. Find the area of quadrilateral ABCD in which AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and ∠ABC = 90º.
(A) 300 cm²
(B) 180 cm²
(C) 126 cm²
(D) 306 cm²
Answer : D

Question. The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.
(a) 4√30
(b) 8√30
(c) 12√30
(d) 16√30

Question. Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm
(a) 1500√3
(b) 3000√3
(c) 4500√3
(d) 6000√3

Question. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
(a) 14√11
(b) 21√11
(c) 35√11
(d) 21√11

Question. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.
(a) 6000
(b) 9000
(c) 12000
(d) none of these

Question. The height corresponding to the longest side of the triangle whose sides are 42 cm, 34 cm and 20 cm in length is
(a) 15 cm
(b) 36 cm
(c) 16 cm
(d) none of these

Question. A park, in the shape of a quadrilateral ABCD, has
(a) 56.4 m²
(b) 55.4 m²
(c) 65.4 m₂
(d) none of these

Question. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
(a) 15 cm²
(b) 15.4 cm²
(c) 15.2 cm²
(d) none of these

Question. If the area of an equilateral triangle is 81 3 cm², then its height is
(a) 9√3
(b) 3√3
(c) 12√3
(d) none of these

Question. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
(a) 45 m²
(b) 48 m²
(c) 51 m²
(d) none of these

Question. The altitude of a triangular field is one-third of its base. If the cost of sowing the field at Rs 58 per hectare is Rs. 783 then its altitude is
(a) 900 m
(b) 600 m
(c) 300 m
(d) none of these

Question. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
(a) 12 cm
(b) 15 cm
(c) 18 cm
(d) none of these

Question. Area of equilateral triangle of side a unit is
(a) √3/2a² 
(b) √3/4a² 
(c)√3/2a
(d) none of these

Question. The height of an equilateral triangle is 6 cm, then the area of the triangle is
(a) 15√3
(b) 3√3
(c) 12√3
(d) none of these

Question. The area of an isosceles triangle each of whose equal sides is 13 m and whose base is 24 m =
(a) 45 m²
(b) 48 m²
(c) 60 m²
(d) none of these

Question. The base of an isosceles triangle is 24 cm and its area is 192 cm², then its perimeter is
(a) 64 cm
(b) 65 cm
(c) 68 cm
(d) none of these

Question. The difference between the sides at right angles in a right angled triangle is 14 cm. If the area of the triangle is 120 cm², then the perimeter of the triangle is
(a) 64 cm
(b) 60 cm
(c) 68 cm
(d) none of these

Question. The base of a triangular field is three times its altitudes. If the cost of sowing the field at Rs 58 per hectare is Rs. 783 then its base is
(a) 900 m
(b) 600 m
(c) 1200 m
(d) none of these

Question. The length of altitude of a equilateral triangle of side a unit is
(a) √3/2a²  
(b) √3/4a² 
(c) √3/2a
(d) none of these

Question. The area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length is
(a) 150 cm²
(b) 336 cm²
(c) 300 cm²
(d) none of these

Question. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle in cm² is.
(a) 9√15
(b) 12√15
(c) 6√15
(d) none of these

Question. The height corresponding to the longest side of the triangle whose sides are 91 cm, 98 cm and 105 cm in length is
(a) 76.4 cm
(b) 78.4 cm
(c) 65.4 cm
(d) none of these

Question. If the area of an equilateral triangle is 36√3 cm², then its perimeter is
(a) 64 cm
(b) 60 cm
(c) 36 cm
(d) none of these

Question. The base of a right angled triangle is 48 cm and its hypotenuse is 50 cm then its area is
(a) 150 cm²
(b) 336 cm²
(c) 300 cm²
(d) none of these

Question. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
(a) 89.4 m²
(b) 89.075 m²
(c) 89.75 m²
(d) none of these

Question. A triangular park ABC has sides 120m, 80m and 50m . A gardener Dhania has to put a fence all around it and also plant grass inside. How much area in m² does she need to plant?

(a) 9√15
(b) 12√15
(c) 6√15
(d) none of these

Question. The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude:
(a) 16√5 cm
(b) 10√5 cm
(c) 24√5 cm
(d) 28 cm

Question. If the area of an equilateral triangle is 16√3 cm², then the perimeter of the triangle is:
(a) 64 cm
(b) 60 cm
(c) 36 cm
(d) none of these

Question. The length of each side of an equilateral triangle having an area of 9√3 cm² is:
(a) 8 cm
(b) 6 cm
(c) 36 cm
(d) 4 cm

Question. The area of an equilateral triangle with side is:
(a) 5.196 cm²
(b) 0.866 cm²
(c) 3.4896 cm²
(d) 1.732 cm²

Question. The sides of a triangle are 56 cm, 60 cm and 52 cm, then the area of the triangle is:
(a) 1322 cm²
(b) 1311 cm²
(c) 1344 cm²
(d) 1392 cm²

Question. The perimeter of an equilateral triangle is 60 m. The area is:
(a) 15√3 m²
(b) 3√3 m²
(c) 12√3 m²
(d) none of these

Question. An isosceles right triangle has area 8 cm², then length of its hypotenuse is
(a) √32cm
(b) √16cm
(c) √48cm
(d) √24cm

Question. A traffic signal board indicating ‘SCHOOL AHEAD’ is an equilateral triangle with side a, then area of the traffic signal is
(a) √3/2a²  
(b) √3/4a² 
(c) √3/2a 
(d) none of these

Question. The base of a triangle is 12 cm and height is 8 cm, then the area of a triangle is:
(a) 24 cm²
(b) 96 cm²
(c) 48 cm²
(d) 56 cm²