Name: Finding Area of Equilateral Triangle
Uploaded: 2019-07-19
Duration: 2 min 54 s
Description: We know that if all sides of a triangle are equal, then it is an equilateral triangle. Is there a formula to find the area of an equilateral triangle? Let's...

Question

Find the area of triangle by counting squares and also by base and height formula. Compare if both the values are equal.

Accepted Answer

Given triangle,

First we will find the area of triangle by counting the squares.

Length of the side of the square is $= 1 c m$

Area of one square is $= 1 c m \times 1 c m = 1 c m^{2}$

Two half square add up to form area equivalent to one square.

In case of square which are more than half we will assume them having area equal to $1 c m^{2}$ .

Number of full square $= 6$

Number of square whose area is more than half $= 2$

Area of full square and square whose area is more than half $= 8 \times 1 = 8 c m^{2}$

Number of half square $= 4$

Area of half square $= \frac{4}{2} \times 1 = 2 c m^{2}$

Total area $= 8 c m^{2} + 2 c m^{2} = 10 c m^{2}$

Now we have to find the area of triangle using formula $= \frac{1}{2} \times$ base $\times$ height

Each side of square has length of $1 c m$ .

For finding the length of base we need to count number of square which comes under it.

Base $= 5 \times 1 c m = 5 c m$

For finding height count the number of squares from base to tip of the triangle.

Height $= 4 \times 1 c m = 4 c m$

Area $= \frac{1}{2} \times 5 \times 4 = 5 \times 2 = 10 c m^{2}$

Hence, we conclude that through both the process we get the same area of triangle which is $10 c m^{2}$ .

West Bengal Board Solutions for Chapter: Properties of Triangle, Exercise 5: Exercise 5

West Bengal Board Mathematics Solutions for Exercise - West Bengal Board Solutions for Chapter: Properties of Triangle, Exercise 5: Exercise 5

Questions from West Bengal Board Solutions for Chapter: Properties of Triangle, Exercise 5: Exercise 5 with Hints & Solutions

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