How to solve geometry problems.

 

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°

In the picture,

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

To find :- <ACD =?

Solution:-

∵ In Δ ABC

∴ ∠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:-

Here,

                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

5. The measures of each equal sides of an isoscles is 4 m and its base is 6 m, find the area of the triangle.

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

∴ Area of the of the isosceles Δ is

    = √ 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.

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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.

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