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# 6. Find the radii of inscribed and circumscribed circle of equilateral triangle if one side of this triangle is a.

## 1. In a triangle ABC, AB=8cm, AC=5cm and

A : B : C 3: 4 :11

## . Find area of the triangle.

3. Radius of inscribed circle of a triangle is 3cm and perimeter of the triangle is 20cm. Find area of the
triangle.
1. In a triangle ABC, BD is height to AC and AB=25cm, BC=26cm, BD=24cm. Find area of the triangle.

3. Radius of inscribed circle of a triangle is 4cm and area of the triangle is 18cm 2. Find perimeter of the
triangle.
1. Perimeter of an isosceles triangle is 36cm and its base is 10cm. Find area of the triangle.

3. Perimeter of an isosceles triangle is 128cm and its base is 48cm. Find radius of inscribed circle of the
triangle
1. Length of lateral side of an isosceles triangle is 17cm and its perimeter is 50cm. Find area of the
triangle.

3. Length of lateral side of an isosceles triangle is 40cm and height to base of the triangle is 32cm. Find
radius of circumscribed circle of the triangle.
1. Perimeter of an equilateral triangle is 36cm. Find area of the triangle which is formed by midlines of
the given triangle.

3. Area of a right triangle is 24cm2 and radius of circumscribed circle of the triangle is 5cm. Find radius of
inscribed circle of the triangle.
1. Height of an equilateral triangle is 12cm. Find area of the triangle which is formed by midlines of the
given triangle.

3. Perimeter of a right triangle is 24cm and radius of inscribed circle of the triangle is 2cm. Find radius of
circumscribed circle of the triangle.
A : B : C 3: 4 : 11
1. In a triangle ABC, AB=8cm, AC=5cm and
. Find area of the triangle.
2. Radius of inscribed circle of a triangle is 3cm and perimeter of the triangle is 20cm. Find area of
the triangle.
1. Perimeter of an isosceles triangle is 36cm and its base is 10cm. Find area of the triangle.
2. Perimeter of an isosceles triangle is 128cm and its base is 48cm. Find radius of inscribed circle of
the triangle.
1. Perimeter of an equilateral triangle is 36cm. Find area of the triangle which is formed by midlines
of the given triangle.
2. Area of a right triangle is 24cm2 and radius of circumscribed circle of the triangle is 5cm. Find
radius of inscribed circle of the triangle.

Fatos Shuli
Maths Teacher

) Find the radius of inscribed circle drawn inside a triangle with side lengths 5cm,6cm and 7cm

5) Find the radius of a circumscribed circle of an isosceles triangle with side lengths
10cm,10cm,12cm
Let r be radius of inscribed circle of a triangle ABC with side lengths a,b,c.
P=a+b+c and u=P/2(semiperimeter)
A(ABC)=u.r
EX: Find r if side lengths of a triangle are 5,12,13

V) Let R be the radius of circumscribed circle of a triangle ABC with side lengths

A(ABC)=

a.b.c
4.R

EX: Find the radius of the circumscribed circle of a triangle whose side lengths are 3cm,4cm
and 5cm

Circles In Triangles:

Fig-1
Fig-2

The circle whose centre is the intersection of the angle bisectors and that is tangent to
sides is called inscribed circle( Fig-1). The center of the circle is called incenter.

The circle whose center is the intersection of the middle perpendiculars and that passes
through the vertices is called circumscribed circle. The center of the circle is called orthocenter.

Fatos Shuli
Maths Teacher

6. Sides of a triangle are 13cm, 14cm and 15cm. Find radii of inscribed and circumscribed circles of the
triangle.

7. Lateral side of an isosceles triangle is 17cm and its height to base is 8cm. Find area of the triangle.
8. Legs of a right triangle are 10cm 26cm. Find length of height to hypotenuse.
9. Height to lateral side of an isosceles triangle divides the lateral side into two parts 8cm and 18cm from
the vertex. Find area of the triangle.
6. Sides of a triangle are 13cm, 14cm and 15cm. Find radii of inscribed and circumscribed circles of the
triangle.

7. Lateral side of an isosceles triangle is 17cm and its height to base is 8cm. Find area of the triangle.
8. Legs of a right triangle are 10cm 26cm. Find length of height to hypotenuse.
9. Height to lateral side of an isosceles triangle divides the lateral side into two parts 8cm and 18cm from
the vertex. Find area of the triangle.

## Every cloud has a silver lining.

Properties

Triangles with equal bases and equal altitudes are equal in area.
A median of a triangle separates the triangle into two triangular regions which have the same area.
The ratio of the areas of triangles with equal altitudes is equal to the ratio of their corresponding bases.
The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides.

Exercises
2. Sides of a triangle are 9cm, 10cm and 11cm. Find radii of inscribed and circumscribed circles of the
triangle.
3. Hypotenuse of a right triangle is 37cm and sum of its legs is 47cm. Find area of the triangle.

GEOMETRY

9th
Form

Worksheet-2

(Area of figures-2 )

Fatos Shuli
Maths Teacher

B
A

Area of a Triangle

1
AC BH
2
AC base, BH height to AC

1. S

1
AC AB sin
BAC

2
3. Heron ' s Formula
2. S

p p a p b p c

p is half perimeter , p

P
2

## 4. S p r ; r is the radius of inscribed circle

a b c
5. S
; R is the radius of circumscribed circle
4R
6. Area of a right triangle
AC AB
S
; AC and AB are legs.
2
7. Area of an equilateral triangle
S

a2 3
a 3
; h
; a is length of one side.
4
2

Fatos Shuli
Maths Teacher

Properties

Triangles with equal bases and equal altitudes are equal in area.
A median of a triangle separates the triangle into two triangular regions which have the same area.
The ratio of the areas of triangles with equal altitudes is equal to the ratio of their corresponding bases.
The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides.

EXERCISES

1. Sides of a triangle are 13cm, 14cm and 15cm. Find radii of inscribed and circumscribed circles of
the triangle.
2. Lateral side of an isosceles triangle is 17cm and its height to base is 8cm. Find area of the
triangle.
3. Legs of a right triangle are 10cm 26cm. Find length of height to hypotenuse.
4. Height to lateral side of an isosceles triangle divides the lateral side into two parts 8cm and 18cm
from the vertex. Find area of the triangle.
5. Sides of a triangle are 9cm, 10cm and 11cm. Find radii of inscribed and circumscribed circles of
the triangle.
6. Hypotenuse of a right triangle is 37cm and sum of its legs is 47cm. Find area of the triangle.
7. Solve the following test questions.

10

45

30

60

3
A
D

.
H

Given AD=IDCI, DHBC, BC=12 and DH=4, what is the area of triangle ABC in cm2.
a)96 b)72 c)64 d) 48 e)24
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