Area Of Triangle Given Sides

Triangle: A plane figure bounded by three line segments is called a triangle.

Types of triangle on the basis of sides:

1) Equilateral trianlge: A triangle having all sides equal is called an equilateral triangle.

2) Isosceles triangle: A triangle having two sides equal is called an isosceles triangle.

3) Scalene triangle: A triangle in which all the sides are of different lengths is called a scalene triangle.

Types of trianlge on the bases of angle:

1) Right-angled triangle: The triangle with a 90 degree angle is said to be right triangle.  The right triangle obeys the Pythagorean Theorem. Here the largest side is said to be hypotenuse and other two sides are said to be legs.

2) Acute-angled triangle: A triangle in which every angle measure more than 0° but less than 90° is called an acute-angled triangle.

3) Obtuse-angled triangle: A triangle in which one of the angles measure more than 90° but less than 180° is called an obtuse-angled triangle.

 Area of triangle:

                When the all sides are given, then area of the triangle is the multiplication of half of base side(adjacent side) and the corresponding height side. Here the base and corresponding height are legs for the given triangle. So area of the triangle is product of legs

 

Formula for area of triangle:

 

Area of right triangle =  `(1/2)` (bh) square .units.

                                  Here b- base

                                   h- Height of the triangle.

                                                                                                                                                                     Area of triangle

 

Hero's formula:

Consider a triangle ABC in which BC = a units, CA =  b units and AB = c units.

       Let s = semiperimeter = $frac{a + b + c }{2}$.

 By Hero's formula, the area of a triangle ABC is given by                                                           

                                         = $qrt{s (s-a)(s-b)(s-c)}$      sq units.

 

Example problems on area of triangle:

 

Ex1: If base side of the triangle is 40 m and height side of the triangle is 50 m, then find the area of the triangle?

 Solution:   Step1:Base side, b= 40m

                               Height side, h = 50m

                    Step2: Formula:  Area of the triangle = `(1/2)` (bh) square. Units

                                                                                       = `(1/2)` (40x50)

                                                                                       = `(1/2) ` (2000)

                                                                                     = 1000 m2

 Ex2: If the base side is 4m and the hypotenuse side is 5m, then find the area of triangle?

 Solution: Step1: Base side = 4m

                              Hypotenuse side = 5m

                   Step2: Since it is right triangle

                                       (Hypotenuse side)2= (base side)2  + (adjacent side)2

                                                          52  = 42+ h2

                                                          25  = 16+ h2

                                                          25 - 16  = h2

                                                          9 = h2

                                                          3 = h

                                  So the height of the triangle is 3 m

                   Step3: Formula: Area of the triangle = `( 1/2)` (bh) square. Units

                                                                                    = $frac{1}{2}$   (4x3)

                                                                                   = `(1/2)` (12)

                                                                                   = 6 m2

 Ex3. Find the area of the triangle when the base side of the triangle is 60 m and height side of the triangle is 20 m?

 Solution: Step1:Base side, b= 60m

                  Step2:Height side, h = 20m

 

                 Step3: Formula: Area of the triangle = `(1/2)` (bh) square. Units

                                                                                   = `(1/2)` (60x20)

                                                                                  = `(1/2)` (1200)

                                                                                    = 600 m2

Ex4: Find the perimeter and area of a triangle whose sides are of lengths 52cm, 56cm and 60cm respectively.

Solution: Step1: Let a = 52cm, b = 56cm and c = 60cm.

                Step2:   Let s = semiperimeter = $frac{a + b + c }{2}$.

                                                                        = $frac{52 + 56 + 60 }{2}$.

                                                                        = 84cm.

                Step3: By Hero's formula, the area of a triangle ABC is given by                                                           

                                         = $qrt{s (s-a)(s-b)(s-c)}$

                        = $qrt{84 (84 - 52)(84 - 56)(84 - 60)}$ 

                        = 1344 cm2.

 

practice problems on area of triangle:

 

Problem1:Find the area of the triangle when the base side of the triangle is 30 m and height side of the triangle is 40 m?

Ans: 600 m2

Problem2:Find the area of the triangle when the base side of the triangle is 10 m and height side of the triangle is 15 m?

Ans:75 m2 .