Ncert exemplar solutions mathematics class 9 Solutions for Chapter 12 herons formula

Exercises in Chapter 12 herons formula Grade 9

Heron's Formula - Exercise 12.1

Heron's Formula - Exercise 12.2

Heron's Formula - Exercise 12.3

Heron's Formula - Exercise 12.4

Questions in Heron's Formula - Exercise 12.1

An isosceles right triangle has area 8 cm². The length of its hypotenuse is

(A) √32 cm

(B) √16 cm

(D) √24 cm

The perimeter of an equilateral triangle is 60 m. The area is

(A) 10√3 m²

(B) 15√3 m²

(D) 100√3 m²

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

(D) 1392 cm²

The area of an equilateral triangle with side 2√3 cm is

(A) 5.196 cm²

(B) 0.866 cm²

(D) 1.732 cm²

Questions in Heron's Formula - Exercise 12.2

Write True or False and justify your answer:

The area of a triangle with base 4 cm and height 6 cm is 24 cm2.

Write True or False and justify your answer:

The area of △ ABC is 8 cm2 in which AB = AC = 4 cm and ∠A = 90º

Write True or False and justify your answer:

The area of the isosceles triangle is 5/4 √11cm², if the perimeter is 11 cm and the base is 5 cm.

Write True or False and justify your answer:

The area of the equilateral triangle is 20√3 cm² whose each side is 8 cm.

Questions in Heron's Formula - Exercise 12.3

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.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

Questions in Heron's Formula - Exercise 12.4

How much paper of each shade is needed to make a kite given in Fig. , in which ABCD is a square with diagonal 44 cm.

The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.

A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.

Find the area of a parallelogram given in Fig. . Also find the length of the altitude from vertex A on the side DC.