Question

Find the area of a square park whose perimeter is $ 320 $ m

Answer 1

Hint: First, we need to know about the perimeter and area concept to solve this problem further.
Since, the area is the determining the boundaries of the given two-dimensional space, which is enclosed within frames of an object.
Perimeter is the total sum of distance covered along with the given outer part of the shape.
The perimeter of the different shapes can be equal to each other.
Formula used:
Perimeter $ = 4 \times a $ where $ a $ is the sides of the given perimeter.
The area of the square equals to the $ {a^2} $

Complete step by step answer:
Since the area of the square park whose perimeter is given as $ 320 $ meters and we need to calculate the total area for the park.
Let us start with the perimeter of the square $ 4 \times a $ , and the area of the perimeter is given as $ 320 $ meters.
Thus, compare both equation we get $ 4a = 320 $ (which is the perimeter of the square)
Hence solving this equation, we get, $ 4a = 320 \Rightarrow a = \dfrac{{320}}{4} \Rightarrow a = 80 $ (by the division operation)
Therefore, we get the sides of the perimeter as $ 80m $
Now applying the area of the square formula, we get; Area of the square equals to the $ {a^2} $
Since we have the $ a = 80m $ then squaring this we get the area of the square.
Hence, we get the area of the square \[ = {a^2} \Rightarrow {(80m)^2}\]
Simplifying the equation with the multiplication operation, we get \[{a^2} = {(80m)^2} \Rightarrow 80m \times 80m \Rightarrow 6400{m^2}\]
Hence, the area of the square park is $ 6400{m^2} $

Note: Since the area and perimeter of the square are given as \[{a^2},4a\] respectively.
Similarly, the area and perimeter of the rectangle are $ a \times b,2(a + b) $ respectively.
The area and perimeter of the triangle are given $ \dfrac{1}{2}b \times h,a + b + c $ respectively, where b is the base and h is the height.