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 200cm ^{2} . 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 :