# KC Sinha Mathematics Solution Class 9 Chapter 14 Areas (Herons formula) exercise 14.1

Page 14.17

### EXERCISE 14.1

Type 1

#### QUESTION 1

Find the area of the triangle whose two sides are 8cm and 11cm and perimeter is 32cm

Sol :

#### QUESTION 2

The base of an isosceles triangle is 12 cm, and each of the equal sides is 10 cm. Find the area of the triangle

Sol :

#### QUESTION 3

(i) The unequal side of an isosceles triangle is 48 cm. and its perimeter is 108 cm. Find the area of the triangle.

(ii) The hypotenuse of a right angled isosceles triangle is 16√2 in f‌ind its area.

Sol :

#### QUESTION 4

The area of right angled isosceles triangle is 200cm2 . Find its hypotenuse .

Sol :

#### QUESTION 5

If one side of an equilateral triangle is 8 m long , then f‌ind the area of the triangle .

Sol :

#### QUESTION 6

(i) The perimeter of an equilateral triangle is 36cm , then find the area of the triangle .

(ii) Find the area of an equilateral triangle whose perimeter is 60cm

Sol :

#### QUESTION 7

(i) If the sides of a triangle are in the rato 25:17:12 and its perimeter is 540cm , then find the area of the triangle .

(ii) The sides of a triangle are in the ration of 13:14:15 . If its perimeter is 84cm , then find the area of the triangle

Sol :

TYPE 2

#### QUESTION 8

The sides of a triangle are 5cm , 12cm and 13cm , find the length of the perpendicular drawn from the opposite vertex on the longest side.

Sol :

#### QUESTION 9

One side of an equilateral triangle is 8√3 ,then find the length of the perpendicular drawn from any vertex on the opposite side

Sol :

#### QUESTION 10

One side of a right angled triangle is 12m . Difference of its hypotenuse and the other side is 8m , then find the lengths of the two sides and its area . Verify the Heron’s Formula

Sol :

#### QUESTION 11

The perimeter of a right angled triangle is 12cm and its hypotenuse is 5cm . Find the length of other two sides and area if the triangle . Verify the result obtained by Heron’s formula

Sol :

#### QUESTION 12

The perimeter of a right angled triangle is 132cm and its hypotenuse is 61cm . Find the length of other sides and area of the triangle.

Sol :

#### QUESTION 13

The side of an equilateral triangle is 16cm . Find its area by Heron’s Formula . What is the height of the triangle ?

Sol :

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