Heron’s Formula For Class 9 Maths MCQ Questions -

Q 1 – An isosceles right triangle has an area of 8 cm². The length of its hypotenuse is

(a) √32 cm
(b) √16 cm
(c) √48 cm
(d) √24 cm

Ans. (a) √32 cm

Q 2 – A square sheet whose perimeter is 32 cm is painted at the rate of Rs. 5 per m². The cost of painting is:
(a) Rs. 320
(b) Rs. 350
(c) Rs. 340
(d) Rs. 160
Ans. (a) Rs. 320

Q 3 – The perimeter of an equilateral triangle is 60 m. The area is
(a) 10√3 m²
(b) 15√3 m²
(c) 20√3 m²
(d) 100√3 m²

Ans. (d) 100√3 m²

Q 4 – The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 70 paise per cm² is
(a) Rs. 17
(b) Rs.16.80
(c) Rs. 7
(d) Rs. 16
Ans. (b) Rs. 16.80

Q 5 – The area of an equilateral triangle with side 2√3 cm is
(a) 5.196 cm²
(b) 0.866 cm²
(c) 3.496 cm²
(d) 1.732 cm²

Ans. (a) 5.196 cm²

Q 6 – The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540cm. The area is:
a. 1000 sq.cm.
b. 5000 sq.cm.
c. 9000 sq.cm.
d. 8000 sq.cm.

Ans. c. 9000 sq.cm.

Q 7 – The length of each side of an equilateral triangle having an area of 9√3 cm² is
(a) 8 cm
(b) 36 cm
(c) 4 cm
(d) 6 cm

Ans. (d) 6 cm

Q 8 – The sides of a parallelogram are 100 m each and the length of the longest diagonal is 160m. The area of a parallelogram is:
a. 9600 sq.m
b. 9000 sq.m
c. 9200 sq.m
d. 8800 sq.m

Ans. a. 9600 sq.m

Q 9 – The area of an equilateral triangle having side length equal to $\frac{√3}{4}$ is:
$(a) \frac{2}{27}sq.cm$
$(b) \frac{2}{15} sq.cm$
$(c) \frac{3}{16} sq.cm$
$(d) \frac{3}{14} sq.cm$

$Ans. (c)\frac{3}{16}sq.cm$

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

Ans. (c) 24√5 cm

Q 11 – Length of the perpendicular drawn on the smallest side of the scalene triangle is
(a) Smallest
(b) Largest
(c) No relation
(d) None
Ans. (c) No relation.

Q 12 – The area of a triangle with base 8 cm and height 10 cm is
(a) 20 cm²
(b) 18 cm²
(c) 80 cm²
(d) 40 cm²
Ans. (d) 40 cm²

Q 13 – The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. The area of the triangle is
(a) 80 cm²
(b) 100 cm²
(c) 50 cm²
(d) 60 cm²
Ans. (d) 60 cm²

Q 14 – The edges of a triangular board are 6 cm, 8 cm, and 10 cm. The cost of painting it at the rate of 9 paise per cm² is
(a) Rs 2.00
(b) Rs 2.16
(c) Rs 2.48
(d) Rs 3.00

Ans. (b) Rs 2.16

Q 15 – The base of a right triangle is 48 cm and its hypotenuse is 50 cm. The area of the triangle is
(a) 168 cm²
(b) 252 cm²
(c) 336 cm²
(d) 504 cm²

Ans. (c) 336 cm²

Q 16 – The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus
are
(a) 48 cm,2320 cm²
(b) 48 cm,1820 cm²
(c) 88 cm, 1320 cm²
(d) 48 cm, 1320 cm²
Ans. (d) 48 cm, 1320 cm²

Q 17 – If the height of a parallelogram having 500 cm² as the area is 20 cm, then its base is of length
(a) 25 cm
(b) 15 cm
(c) 20 cm
(d) 50 cm
Ans. (a) 25 cm

Q 18 – The area of a triangle is 150 cm² and its sides are in the ratio 3: 4: 5. What is its perimeter?
a. 10 cm

b. 30 cm

c. 45 cm

d. 60 cm

Ans. d. 60 cm

Q 19 – A carpenter had to make a triangle with sides 5, 6, 5 units. By mistake, he made one with sides 5, 8, 5 units. The difference between their areas is:

(a) 16 sq units

(b) 2 sq units

(c) 4 sq units

(d) 0 sq units

Ans. (d) 0 sq units

Q 20 – What in the area of an equilateral triangle with side 2 cm?
a. √6 cm²

b. √3 cm²

c. √8 cm²

d. 4 cm²

Ans. b. √3 cm²

Q 21 – The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is
(a) 1322 cm²
(b) 1311 cm²
(c) 1344 cm²
(d) 1392 cm²

Ans. (c) 1344 cm²

Q 22 – What is the length of each side of an equilateral triangle having an area of 4√3 cm² ?
a. 4 cm

b. 5 cm

c. 5 cm

d. 6 cm

Ans. a. 4 cm

Q 23 – The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of the triangle is 84 cm, then area of the triangle is :
(a) 294 cm²
(b) 290 cm²
(c) 274 cm²
(d) 252 cm²
Ans. (a) 294 cm²

Q 24 – The sides of a triangle are 3 cm, 5 cm and 6 cm. What is its area?
a. 2√3cm²

b. 2√14cm²

c. 5√12cm²

d. 2√5cm²

Ans. b. 2√14cm²

Q 25 – If the side of a scalene △ is doubled then the area would be increased by
(a) 300 %
(b) 150 %
(c) 125 %
(d) None of these
Ans. (a) 300 %

Q 26 – What is the area of an equilateral triangle with side √3/2 cm?
a. 2/27 cm²

b. 2/15 cm²

c. 3√3/16 cm²

d. none of these

Ans. c. 3√3/16 cm²

Q 27 – The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Its area is
(a) 2598. 08m²
(b) 5598. 08m²
(c) 8598. 08m²
(d) 6598. 08m²
Ans. (a) 2598. 08m²

Q 28 – The length of one of the equal sides of an isosceles triangle is 4 cm. If its base be is 2 cm then what is its area?
a. √15 cm²

b. √13 cm²

c. √12cm²

d. √14cm²

Ans. a. √15 cm²

Q 29 – Given the product of diagonals of a rhombus ABCD is 2500 cm², its area is
(a) 1250 cm²
(b) 625 cm²
(c) 1200 cm²
(d) 2000 cm²
Ans. (a) 1250 cm²

Q 30 – 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

Ans. 48 cm²

Q 31 – If each side of an equilateral triangle is increased by 2 cm, then its area increases by 3√3 cm2. The length of its each side and its area are respectively equal to
(a) 3 cm, √3cm²
(b) 2 cm, √3cm²
(c) 2 cm, √8 cm²
(d) 2 cm, √5 cm²
Ans. (b) 2 cm, √3cm²

Q 32 – The sides of a triangle are 8 cm, 11 cm and 13 cm. What is its area?
a. 8√30 cm²

b. 4√10 cm²

c. 3√100 cm²

d. 6√200 cm²

Ans. a. 8√30 cm²

Q 33 – Find the length of each side of an equilateral triangle having area of 9 root 3 cm square
(a) 36 cm
(b) 5 cm
(c) 15 cm
(d) 6 cm
Ans. (d) 6 cm

Q 34 – The sides of a triangle are 15 cm, 17 cm and 8 cm. What is its area?
a. 20 cm²

b. 40 cm²

c. 60 cm²

d. 80 cm²

Ans. c. 60 cm²

Q 35 – The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm² is
(a) Rs 2.00
(b) Rs 2.16
(c) Rs 2.48
(d) Rs 3.00

Ans. (b) Rs 2.16

Q 36 – The sides of a triangle are in the ratio of 3: 4: 5. If its perimeter is 36 cm, then what is its area?
a. 32 cm²

b. 54 cm²

c. 67 cm²

d. 72cm²

Ans. b. 54 cm²

Q 37 – The difference of the semi-perimeter and the sides of △ABC are 8, 7 and 5 cm respectively. Its semi-perimeter ‘s’ is
(a) 20 cm
(b) 5 cm
(c) 15 cm
(d) 10 cm
Ans. (a) 20 cm

Q 38 – 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

Ans. c. 24√5 cm

Q 39 – The base of a right triangle is 48 cm and its hypotenuse is 50 cm. The area of the triangle is
(a) 168 cm²
(b) 252 cm²
(c) 336 cm²
(d) 504 cm²

Ans. (c) 336 cm²

Q 40 – If the area of an equilateral triangle is 16√3 cm², then the perimeter of the triangle is:
a. 24 cm

b. 60 cm

c. 36 cm

d. none of these

Ans. a. 24 cm

Q 41 – The base of a right-angled triangle with an area 300 cm² and height 30 cm is
(a) 10 cm
(b) 30 cm
(c) 20 cm
(d) 15 cm
Ans. (c) 20 cm

Q 42 – An isosceles right triangle has area 8 cm², then length of its hypotenuse is:
a. √32 cm

b. √16 cm

c. √48 cm

d. √24 cm

Ans. a. √32 cm

Q 43 – The area of a right triangle of height 15 m and base 20 m is
(a) 160 m²
(b) 150 m²
(c) 210 m²
(d) 216 m²
Ans. (b) 150 m²

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