Calculating the Square's Area Using Pole Information
The problem asks for the area of a square fence constructed using 48 poles, with each pole spaced 5 meters apart.
Perimeter Calculation
For a closed shape like a square, the number of intervals between poles is equal to the number of poles. Therefore, 48 poles create 48 intervals along the perimeter.
- Number of poles = 48
- Distance between poles = 5 m
- Number of intervals = 48
- Perimeter = Number of intervals $\times$ Distance between poles
- Perimeter = $48 \times 5 \text{ m} = 240 \text{ m}$
Side Length Determination
A square has four equal sides. The perimeter is the total length of all sides.
- Perimeter of a square = $4 \times \text{side length}$
- $240 \text{ m} = 4 \times \text{side length}$
- Side length = $\frac{240 \text{ m}}{4} = 60 \text{ m}$
Area Calculation
The area of a square is calculated by squaring its side length.
- Area = $(\text{side length})^2$
- Area = $(60 \text{ m})^2$
- Area = $3600 \text{ m}^2$
The area of the square formed is $3600 \text{ m}^2$. This corresponds to Option B.
Similar Questions
- A square is inscribed in a circle which is inscribed in an equilateral triangle. If one side of the triangle is $x$, then the area of square is:
- A path around the inner side of a rectangular park measuring $37\text{ m} \times 30\text{ m}$ occupies $570\text{ m}^{2}$. What is the width of the path?
- The two unequal sides of a rectangle are in the ratio of 3 : 4. If the perimeter is 42 cm, then the length of diagonal will be:
- Four cows are tethered to the four corners of a square field of length 28 m so that each cow can just touch the two cows in the adjacent corners. If the grass in the area inside the square field that was accessible to the cows was enough to feed them for 22 days, for how many days would the grass that is beyond the reach of these cows be able to feed them if someone cuts it and leaves it inside the grazable parts? [Use $\pi = 22/7$]
- What is the area of a rhombus, whose sides are 25 cm and one of the diagonals is 14 cm?
- A sector of a circle has a radius of $18\text{ cm}$ and a central angle of $125^\circ$. What will be its approximate perimeter?
(Use $\pi = \frac{22}{7}$) - 30 ml paint is required to paint a circular plate of 20 cm radius. How much paint is required to paint a similar plate of radius 80 cm?
- If the length and the perimeter of a rectangle are in the ratio of 3 : 20, then its length and breadth will be in the ratio of:
- A wire in the form of a circle of radius 56 m is cut and again bent in the form of a square. What is the measure of the diagonal of the square?
- There is a regular hexagon of side 5 cm. Find its area.
Important Questions from 2-D Mensuration
- The length of a rectangular plot is $(x^2 + xy + y^2)$ m and its breadth is $(x^2 - 5xy - y^2)$ m.
Find its perimeter, when $x = 1$ and $y = -1$. - The ratio between the perimeter and breadth of a rectangle is 3: 1. If the area of the rectangle is $98 \text{ cm}^2$, find the perimeter (in cm) of the rectangle.
The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
