CBSE Class 9 Mathematics Herons Formula Assignment Set A

Question. The perimeter of at riangular 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
Answer : A

Question. The perimeter of a rhombus is 52 cm and one of it s diagonals is 24 cm. Det ermine the length of the other diagonal.
(A) 24 cm
(B) 10 cm
(C) 2(1/6) cm
(D) 12 cm
Answer : B

Question. The area of a rhombus is 28 cm² and one of it s diagonals is 4 cm. What is its perimeter?
(A) 4√S3 cm
(B) 36 cm
(C) 2√S3 cm
(D) 52 cm
Answer : A

Question. The adjacent sides of a parallelogram are 8 cm and 9 cm. The diagonal joining the ends of these sides is 13 cm. Find its area.
(A) 72 cm²
(B) 12√35 cm²
(C) 24√35 cm²
(D) 150 cm²
Answer : B

Question. The sides of at riangle are 11 cm, 15 cm and 16 cm . Find the measure of the altitude to the largest side.
(A) 30√7 cm
(B) 15√7 cm
(C) 15√7 cm
(D) 30m
Answer : C

Question. The base of an isosceles t riangle is 12 cm and it s perimeter is 32 cm. What is its area?
(A) 12 sq.cm
(B) 36 sq.cm
(C) 24 sq.cm
(D) 48 sq.cm
Answer : D

Question. 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) ₹ 2.00
(B) ₹ 2.16
(C) ₹ 2.48
(D) ₹ 3.00
Answer : B

Question. 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
Answer : A

Question. Two adjacent sides of a parallelogram are 5 cm and 3.5 cm. One of it s diagonals is 6.5 cm. Find the area of parallelogram.
(A) 5√3 cm²
(B) 100√3 cm²
(C) 15√3 cm²
(D) 20√3 cm²
Answer : B

Question. The perimeter of a t riangle is 60 m and its sides are in t he ratio 5 : 12 : 13, Find the  length of the altitude of the triangle corresponding to the longest side.
(A) 9(3/13)m
(B) 5(4/12)m
(C) 6(9/11)m
(D) 7(2/15)m
Answer : A

Question. If the alt it ude of an equilateral triangle is √6 em, what is its area?
(A) 2√3 cm²
(B) 2J2 cm²
(C) 3J3 cm²
(D) 6J2 cm²
Answer : A

Question. The perimeter of an equilateral triangle is 60 m. What is its area?
(A) 10√3m²
(B) 15√3m²
(C) 20√3m²
(D) 100√3m²
Answer : D

Question. The sides of an equilateral triangle are (2a - b + St (a +b) and (2b - a+ 2). What is the area of the triangle?
(A) √3/4 x a²
(B) √3/4 x b²
(C) √3/4 x 49
(D) √3/4 x 81
Answer : C

Question. In ΔABC,AB = 6 em, BC = 7 cm and AC = 5 cm. What is the area of ΔABC?
(A) 6√6cm²
(B) 6√3cm²
(C) 6√2cm²
(D) 9√6cm²
Answer : A

Question. 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
Answer : A

Question. The base of an isosceles right triangle is 30 cm. Find its area.
(A) 225 cm²
(B) 22S√3 cm²
(C) 225√2 cm²
(D) 450 cm²
Answer : D

Question. One side of an equilateral triangle is 8 cm.
What is its area?
(A) 12√3 cm²
(C) 8√3 cm²
(B) 16√3 cm²
(D) 48√3 cm²
Answer : B

Question. 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
Answer : C

Question. What is the area of a parallelogram whose diagonal is 6.8 em and the perpendicular distance of this diagonal from an opposite vertex is 7.5 cm?
(A) 25.5 cm²
(B) 11.9 cm²
(C) 12.5 cm²
(D) 51 cm²
Answer : D

Question. A farmer divided his field which is in the shape of a rhombus of side 100m between his two sons equally. If the line of division is 160 m, what area of the field did each son get?

(A) 4840 sq m
(B) 1400 m²
(C) 4800 m²
(D) 3600 m²
Answer : C

Question. The sides of a triangle are 50 cm, 78 em and 11 2 cm. Find the smallest altitude.
(A) 20 cm
(B) 30 cm
(C) 40 cm
(D) SO cm
Answer : B

Question. ΔABC is an equilateral triangle where each side is of length 'a' unit s. Find its area if it s perimeter is 150m.
(Al 1000√3 m²
(B) 250√3 m²
(C) 500√3 m²
(D) 625√3 m²
Answer : D

Question. If the area of an isosceles right triangle is 8 cm², what is its perimeter?
(A) (8 + √2) cm
(B) (8 + 4√2) cm
(C) (4 + 8√2) cm
(D) 12√2 cm
Answer : B

Question. The adjacent sides of a parallelogram are 4 cm and 9 cm. What is the ratio of its alt itudes?
(A) 16: 81
(B) 9 : 4
(C) 2 : 3
(D) 3 : 2
Answer : B

Question. Which of the following is the area of an isosceles t riangle wit h equal sides b and base a?
(A) a/2 √b² - a²
(B) 1/2 a√4b² - a²
(C) a/4 √b² - a²
(D) a/4 √b² - a²
Answer : D

Question. An isosceles right triangle has area 8 cm².
What is the length of its hypo-tenuse?
(A) √32cm
(B) √16cm
(C) √48cm
(D) √24cm
Answer : A

Question. A square and an equilat eral triangle have equal perimeters. If the diagonal of the square is 12J2 cm, what is the area of the triangle?
(A) 24√2 cm²
(B) 24√3 cm²
(C) 48√3 cm²
(D) 64√3 cm²
Answer : D

Question. A rhombus shaped field has green grass for 48 cows t o graze. If each side of the rhombus is 50 m and its longer diagonal is 80 m, how much area of the grass field will each cow be able to graze in?
(A) 150 cm²
(B) 120 cm²
(C) 50 cm²
(D) 100 cm²
Answer : C

Question. Suman made an arrangement with  shaded and unshaded paper sheets as shown in the figure.

Find the total area of the shaded paper sheets used in making the arrangement.
(A) 9/4√55 cm²
(B)  8/5√11cm²
(C) 16/9√155 cm²
(D) 6/5√11cm²
Answer : A

Question. The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Find it s area.
(A) 25 cm²
(B) 28 cm²
(C) 30 cm²
(D) 40 cm²
Answer : C

Question. 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√2 cm²
(D) 16√2 cm²
Answer : B

Question. What is the area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm?
(A) √15 cm²
(B) √15/2 cm²
(C) 2√1S cm²
(D) 4√15 cm²
Answer : A

Question. A triangle and a parallelog ram have the same base and the same area.lf 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
Answer : B

Question. What is the length of each side of an equilateral triangle having an area of 9√3 cm² ?
(A) 8 cm
(B) 36 cm
(C) 4 cm
(D) 6 cm
Answer : D

Question. What is the area of a triangle having two sides as 18 cm and 10 cm and perimeter is 42 cm?
(A) 3√11 cm²
(B) 711 cm²
(C) 33√7 cm²
(D) 21√11 cm²
Answer : D

Question. A kite in the shape of a sq uare with a diagonal 40 em and an isosceles triangle of base 10 em and side 13 cm each is to be made of three different shades as shown in the figure. Find t he ratio of each shade used in making the kite.

(A) 20:20:3
(B) 10:10:3
(C) 25:35:3
(D) 9:11:1
Answer : A

Question. What is the semiperimeter of a scalene triangle of sides k, 2k and 3k?
(A) k
(B) 2k
(C) 3k
(D) 4k
Answer : C

Question. The length of the sides of ΔABC are consecutive integers. If Δ ABC has the same perimeter as an equilateral triangle  with a side of length 9 cm, what is the length of the shortest side of ΔABC?
(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm
Answer : C

Question. An umbrella is made by stitching 12 triangular pieces of cloth of two different colours as shown in figure. Each piece measures 40 cm, 40 em and 18 cm.

How much cloth of each colour is required for the umbrealla?
(A) 378√3 cm²
(B) 756√3 cm²
(C) 252√3 cm²
(D) 567√3 cm²
Answer : A

Question. If the area of an equilat eral triangle is 16√3 cm², what is the perimeter of the triangle?
(A) 48 cm
(B) 24 cm
(C) 12 cm
(D) 306 cm
Answer : B

Question. Which of the following should we have in order t o 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
Answer : D

Question. If the length of a median of an equilateral triangle is x em, find its area.
(A) x² cm²
(B) (x²/√3) cm²
(C) (√3/2)x cm²
(D)  (x²/2) cm²
Answer : C

Question. A floral design on a floor is made up of 16 triangular tiles of sides 26 em, 20 cm and 10 em. The tiles are polished at the rate of 20 p per cm².

Find the cost of polishing the t iles.
(Take √14 = 3.74.)
(A) ₹ 195.64
(B) ₹ 216.52
(C) ₹ 287.23
(D) ₹ 325.13
Answer : C

SECTION A: (2 MARKS)

1. The area of an equilateral triangle √16 3 cm². Find its perimeter.  24 cm

2. Find the area of an isosceles triangle having base 2cm and the length of one of the equal sides 4cm. √15 cm² 

3. If the base of a triangle is doubled and the corresponding altitude is tripled. Find the ratio of the new area to the previous area. 6:1

SECTION B: (2 MARKS)

4. The base of a right triangle ABC is 16 cm and hypotenuse is 34 cm. Find the area of the triangle.  240 cm²

5. U sing Heron’s formula, find the area of an equilateral triangle with side 4a units. 4a2 √3

6. The edges of a triangular board are 6cm, 8cm and 10cm. Find the cost of painting it at the rate of Rs 90 per cm2  Rs. 2160

7. The semi-perimeter of a triangle is 132 cm. The product of the difference of semi-perimeter and its respective sides is 13200 cm. Find the area of the triangle. 1320cm²

SECTION C: (3 MARKS)

8. Find the area of a rhombus whose one side is 20 m and one diagonal is 24 m. 384m²

9. If each side of any triangle is doubled then find the percentage increase in its area. 300%

10. If each side of an equilateral triangle is tripled then find the percentage increase in its area. 800%

11. A field is in the shape of a trapezium having parallel sides 90m and 30m.These sides meet the third side at right angles. The length of the fourth side is 100 m. If it cost Rs 4 to plough 1m2 of the field, find the total cost of ploughing the field. Rs 19200

SECTION D: (4 MARKS)

12. Calculate the area of the shaded region in the fig 1,given below 54cm² 

13. In a rectangular field of dimensions 125 m x 80 m, a triangular park is constructed. If the dimensions of the park are 50 m, 78 m and 112 m. Find the area of the remaining field. 8320m² 

14. The lengths of two adjacent sides of a parallelogram are 17 cm and 12 cm. One of its diagonal is 25 cm long. Find the area of the parallelogram. Also find the length of the altitude from vertex on the side of length 12 cm. A= 90cm2 h = 15cm

15. In the fig 2, △ABC has sides AB = 41 cm, AC = 15 cm and BC = 28 cm. On BC a parallelogram DBCE of the same area as that of △ABC is constructed. Find the height of the parallelogram.  h=4.5cm

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