Chapter 3, Problem 9RP

To determine

To Find: The area of given triangle ABC from the given figure.

Answer to Problem 9RP

Area of $\Delta ABC=8$

Explanation of Solution

Given information:

We are given a $\Delta ABC$ drawn on a square graph sheet

Formula Used: $\text{Area of ΔABC = }\frac{\text{1}}{\text{2}}\text{ × base × height}$

Calculation:

As per the question we have been given a $\Delta ABC$ drawn on a square graph sheet. Find the distance between B and C by counting squares (Taking side of each square as $1$ ).

Here we noticed that there are three complete squares and two halves on the base line between B and C.

Thus, the base of $\Delta ABC=\mathrm{4.....................................................}(\text{i)}$

Counting the length of altitude by same method we noticed in the figure it covers four complete square.

Thus, the altitude or height $\Delta ABC=\mathrm{4...........................................}(\text{ii)}$

Taking values from (i) and (ii) and substituting them in the above formula:

Area of triangle will be:

  →$\begin{array}{l}\text{= }\frac{\text{1}}{\text{2}}\text{ × base × height}\\ =\frac{1}{2}\times \text{ 4 }\times \text{ 4}\\ =\frac{16}{2}\\ =\text{ 8}\end{array}$

Which is the required answer.

Conclusion:

  $$ Area of $\Delta ABC=8$