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 54 $cm^2$ .The height of triangle is 6 cm. Calculate the base of triangle.

Solution: According to question

Area of triangle=54 $cm^2$

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

The sides of a triangle are 16 cm, 30 cm and 34 cm. Its area is _________________.
A. 120 $cm^2$		B. 260 $cm^2$
C. 240 $cm^2$		D. 272 $cm^2$
Right Option : C
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Question : 2

Find the area of right triangle if base of triangle is 4.5 m and height is 3.8 m.
A. 8.55 sq m	B. 9.55 sq m	C. 7.56 sq m	D. 8.45 sq m
Right Option : A
View Explanation

Question : 3

If area of a triangle is 20 $cm^{2}$ and base is 20 cm, its height will be ___________________. ,
A. 8 cm		B. 2cm
C. 6 cm		D. 5 cm
Right Option : B
View Explanation