Area of Triangle


 
 
Concept Explanation
 

Area of Triangle

Area of Triangle:

A triangle is a three sided figure. To find the area of triangle we should know the base and the corresponding height of the triangle. The formula is

 Area;of;triangle=frac{1}{2}times basetimes height

In the figure given below

The area of triangle DGF can be calculated as

Area;of;triangle DGF=frac{1}{2}times GFtimes DE

Here DE is perpendicular to the base GF. So we can say that DE is the corresponding height to the base GF.

Illustration: Area of a triangle is 54cm^2.The height of triangle is 6 cm. Calculate the base of triangle.

Solution:   According to question

Area of triangle=54cm^2

Height=6cm

To calculate the base we will use the formula

Area;of;triangle=frac{1}{2}times basetimes height

54=frac{1}{2}times basetimes 6

54=3times base

Base=frac{54}{3}= 18;cm

Area of Right Triangle:

A right triangle is the one in which the measure of any one of the interior angles is 90 degrees. It is to be noted here that since the sum of interior angles in a triangle is 180 degrees, only 1 of the 3 angles can be a right angle. The figure below is a right angled triangle right angled at B.

To calculate the are of a right triangle we will use the two sides which are making an angle of 900. In the above figure angle B is formed with the help of the sides AB and AC. So these sides can be used as base and the corresponding height.. So the are can be calculated as.

Area;of;triangle ;ABC=frac{1}{2}times ABtimes BC

Sometimes we are supposed to calculate the area of a right triangle in which one side and the hypotenuse is given.

In such a situation to calculate the are first we have to calculate the other side using Pythagoras Theorem

Pythagoras Theorem defines the relationship between the three sides of a right angled triangle. Thus, if the measure of two of the three sides of a right triangle is given, we can use the Pythagoras Theorem to find out the third side.

Hypotenuse^2=Perpendicular^2+Base^2

Hypotenuse is the side opposite to the right angle in a triangle.

 

Illustration: Find The Area Of A Right Triangle as given: AB = 4cm and AC = 3cm

Solution:  using Pythagoras theorem,

       (AC)^{2}=(AB)^{2}+(BC)^{2}

      (BC)^{2}=(AC)^{2}-(AB)^{2}

     (BC)^{2}=25-16

      (BC)^{2}=9

     BC=sqrt{9}

      BC = 3 cm

Area of triangle=

  =frac{1}{2}times AB times BC

 =frac{1}{2}times 4 times 3=6cm^2

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Height and base of a triangle are 10ft and 15ft  respectively. Area of the triangle is __________________

Right Option : D
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Explanation
Question : 2

Find the area of a right triangle, whose hypotenuse is 25 cm and base is 15 cm.

Right Option : D
View Explanation
Explanation
Question : 3

Area of a triangle is large 24cm^2 .The height of triangle is 6 cm. The base of triangle is equal to __________

Right Option : B
View Explanation
Explanation
 
 
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