Question

e) The length of a square banquet hall is 30 m and 3/4
of its area is occupied by a banquet stage Find the area of the stage. ​

Answer 1

Answer:

The area of the banquet stage is $\sf  675 \, \textsf{m}^2$

Step-by-step explanation:

Let's denote the length of the square banquet hall as $\sf  L$. The area of a square is given by the formula:
$\sf  \textsf{Area} = L^2$

Given that the length of the square banquet hall is $\sf  30$ meters, we can substitute $\sf  L = 30$ into the formula:

$\sf  \textsf{Area} = (30)^2$

$\sf  \textsf{Area} = 900 \, \textsf{m}^2$

Now, since $\sf  \dfrac{3}{4}$ of the area is occupied by the banquet stage, we can find the area of the stage by multiplying the total area by $\sf  \dfrac{3}{4}$:

$\sf  \textsf{Area\_stage} = \dfrac{3}{4} \times 900 \, \textsf{m}^2$

$\sf  \textsf{Area\_stage} = \dfrac{3}{4} \times 900$

$\sf  \textsf{Area\_stage} = 675 \, \textsf{m}^2$

So, the area of the banquet stage is $\sf  675 \, \textsf{m}^2$.

Answer 2

Answer:

675 m²

Step-by-step explanation:

The area of a square is found by squaring its side length:

$\boxed{\begin{array}{l}\underline{\textsf{Area of a square}}\\\\\Large\text{ A=s^2 }\\\\\textsf{where :}\\\phantom{ww}\bullet\;\textsf{ A is the area.}\\\phantom{ww}\bullet\;\textsf{ s is the side length}.\end{array}}$

Given that the area of the banquet stage is 3/4 of the area of the square banquet hall, then:

$\textsf{Area of banquet stage}=\dfrac{3}{4}s^2$

Since the side length of the square banquet hall is 30 m, we can find the area of the stage by substituting s = 30 into the equation:

$\begin{aligned}\textsf{Area of banquet stage}&=\dfrac{3}{4}(30)^2\\\\&=\dfrac{3}{4}\cdot 900\\\\&=\dfrac{2700}{4}\\\\&=675\; \sf m^2\end{aligned}$

Therefore, the area of the banquet stage:

$\huge\boxed{\boxed{675\; \sf m^2}}$