Question

Four cows are tethered with the rope of equal length 28 m. One on each vertices of a square plot of side 56 m. Each cow can reach the other two along side of square plot. What area will be left uncovered?

Answer 1

Answer:

Step-by-step explanation:

The cows graze around the corners of the square plot.

They follow a circular path.

The ropes represent the radius of the circle the cows graze on.

Since it is on the corners the circle is a quarter a circle given that the angle subtended is 90°

To get the area remaining, we need to get the area of the square plot then subtract the area of the corners of the square.

The areas at the corners are equal.

Area of the corners equal :

= 1/4 × 22/7 × 28^2 = 616 square meters.

Since the four corners have equal areas we have the total areas of the corners as :

4 × 616 = 2464 square meters.

The area of the square plot equals to :

56 × 56 = 3136 square meters.

The area uncovered is thus :

3136 - 2464 = 672 square meters.

Answer 2

Answer:  672 square meter

Step-by-step explanation:

The area that is left = The area of square having side 56 m - 4 × ( area of a 1/4th part of a circle having the radius 28 m)

= $56 \times 56 + 4\times \frac{1}{4} \pi (28)^2$

= $3136 + \frac{22}{7}\times 784$

= $3136 - 2464$

= $672\text{ square m}$