Question

If the area of one square is $1$ square unit then find the areas of the following figure by counting the squares.

Answer 1

Hint: Square is a two-dimensional geometrical figure or square can be defined as by multiplying the number twice. For example, if we want to find the square of $4$ that means we multiply $4$ twice which means $4 \times 4 = 16$. So, the square of $4$ is $16$ and hence, we can say that square can be found by multiplying the number twice. If I have a square plot having $2$cm side each. Also, the sides of the square are equal. Therefore, square having area which is equal to \[side \times side\] that implies $2 \times 2 = 4$ $c{m^2}$

Complete step-by-step answer:
We are given that area of one square is $1$ square unit (where unit may be cm, m etc)
Then, we have to find the area of the given figure by counting the squares.

Since, the figure is made up of $2$ full squares and $4$ half squares. Also, the area of one square is $1$ square unit. Therefore, area of square $BDEF$ and $DHFG$ is $1$ unit each and area of $ABD$ can be written as half of the whole square which means $\dfrac{1}{2}$ square unit.
Therefore, the area of $ABD,ADH,BCE,HIG$ is $\dfrac{1}{2}$ \[\;square{\text{ }}unit\].
Therefore, area of whole figure $ = $ area of $ABD + $ area of $ADH + $ area of $BCE + $ area of $HIG + $ area of $BDEF + $ area of $DHFG$
\[ \Rightarrow \] $ \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2} + 1 + 1$
\[ \Rightarrow \] $ 1 + 1 + 1 + 1$
 $\because \dfrac{1}{2} + \dfrac{1}{2} = 1$
\[ \Rightarrow \] $ 4$ square units

Therefore, the area of whole figure $ = 4$ square units.

Note: The units of area are centimetre square(${c{m^2}}$) and metre square(${m^2}$ )in which the side is given. If the side is in cm then the area is in (${c{m^2}}$) and if the side is in m then the area is in ${m^2}$. Square of a negative number or quantity is also positive. A square is a quadrilateral. We can also find the square of rational numbers like the square of $\dfrac{1}{2}$ is $\dfrac{1}{4}$.