## How to solve geometry problems.

### Today in this article i will show you how to solve various geometry problems.

## Problems of exterior angle of Triangles:-

1.From the picture, Find <ACD=? If <A= 50°and <B=60°

ABC is a triangle, whose <A =50°; <B =60°

To find :- <ACD =?

### Solution:-

∴ ∠ACD = <A + <B [∵sum of two remote interrior angles of a Δ is always equal to its exterior angle]

= 50°+ 60°

= 110°

2. From the picture, Find <BAD, if <B = 60°

<C=70°

In the picture,

ABC is a triangle, whose <B = 60° and <C =70°;

To find :- <BAD =?

### Solution:-

∵ In Δ ABC,

∴ ∠BAD = <B+<C[∵ sum of two remote interrior angles of a Δ is equal to exterior angle]

= 60° + 70°

= 130°

3. In the picture, <Z=100° <Y= 40° then find <X=?

In the picture,

XYZ is a Δ ,whose <Z = 100°,<Y= 40°

To find:- <X = ?

### Solution:-

∴ ∠X+<Y=<Z [∵ sum of two remote interrior angles is equal to exterior angle]

=> <X + 40° = 100°

=> <X = 100° - 40°

=> <X = 60°

4. From the figure, find x=? and y = ?

### Answer:-

From the figure,we will find the values of x=? and y = ?

∵ x = y [∵ vertically opposite angles]...(1)

∵ x = p [ ∵ vertically opposite angles]...(2)

also q = x[∵ vertically opposite angles]...(3)

Now,

x+ p +q = 180° [ ∵ sum of three angles of a Δ is 180°]

=> x + x + x = 180° [ using (1),(2), and (3)]

=> 3x = 180°

=> x = 180°/3

=> x = 60°

Again,

from (1)

y = x

=> y = 60° [putting the value of x]

∴ Requird x = 60°

y = 60°

## Area problems of triangles:-

1.If height of a triangle is 4 cm, and it's base is 7cm, find it's area.

### Answer:-

height of triangle(h) = 4cm

base(b) = 7 cm

∴ Area of the triangle(A) = ½ b.h

=½.4.7

= 2×7 cm²

= 14 cm²

2. The area of a triangle is 40 m² and its height 5m then find its base.

### Answer:-

Here,

Area of the triangle(A) = 40 m²

height of the triangle(h)= 5 m

∴ base of the triangle(b) = 2×A /h

=(2×40)/5 m

= 2×8 m

= 16 m.

3. Area of a triangle is 100 m² its base 8 m

then,find its height.

### Answer:-

Here,

Area of the triangle (A) = 100 m²

base of the triangle(b) = 8 cm

∴ Height of the triangle(h) =( 2×A)/b

= 2×100/8

= 200/8

= 25 m

4. Find the area of an equilateral triangle, whose each side is 8 cm.

### Answer:-

Each side of the equilateral Δ(a)

= 8 cm

∴ Area of the equilateral Δ =√3/4 a²

= (√3×8×8)/4

= √3 ×8×2 cm²

= 16√3 cm²

### Answer:-

Here,

∵Isosceles Δ has two equal sides.

∴1st side of isosceles Δ (a)= 4m

∴ 2nd side of isosceles Δ (b) =4m

and 3rd side of the Δ(c) = 6 m

Now,

Semi perimeter/half perimeter of the Δ(s)

= (a+b+c)/2

= (4+4+6)/2

= 14/2

= 7 m

= √ s.(s-a)(s-b)(s-c)[∵Using Heron's formula]

= √ 7.(7-3).(7-3)(7-6)

=√ 7.4.4.1

= 4√7m²

6. The three different sides of a scalene triangle is 3cm, 4cm and 5cm find its area.

## FREQUENTLY ASKED QUESTIONS:-
## How many exterior angles can have a triangle?

Answer:- Three.

## What is the area formula of an equilateral triangle?

Answer :- Area formula of an equilateral triangle = √3/4 × a²
where, a = measure of each side of the triangle.

## What is the sum of all exterior angles of a triangle?

Answer:- 360°

## What is the relation between interior angle and exterior angle of a triangle?

Answer:- The relation is :-
Exterior angle = Sum of two remote interior angles of a triangle.

##
What is Heron's formula?

Answer :- Area of a scalene
triangle = √(s-a)(s-b)(s-c)
where,s = half perimeter or semi perimeter of scalene triangle ,
and a,b, and c are i measure of it's three sides. This is known as Heron's formula of finding area of a scalene triangle.

## How many exterior angles can have a triangle?

Answer:- Three.

## What is the area formula of an equilateral triangle?

Answer :- Area formula of an equilateral triangle = √3/4 × a² where, a = measure of each side of the triangle.

## What is the sum of all exterior angles of a triangle?

Answer:- 360°

## What is the relation between interior angle and exterior angle of a triangle?

Answer:- The relation is :- Exterior angle = Sum of two remote interior angles of a triangle.

## What is Heron's formula?

Answer :- Area of a scalene triangle = √(s-a)(s-b)(s-c) where,s = half perimeter or semi perimeter of scalene triangle , and a,b, and c are i measure of it's three sides. This is known as Heron's formula of finding area of a scalene triangle.