Question

ABCD is a square of side 14 cm with centers A,B,C and D four circles are drawn such that each circle touch externally two of the remaining three circles find the area of remaining of the square

Answer 1

Answer:

Remaining area of the square = 42 cm²

Explanation:

The given problem can be visualized using the attached diagram. We are asked to find the remaining area of the square which corresponds to the shaded area in the diagram

Area of shaded region = area of square - areas of the 4 quadrants of circles

1- getting the area of the square:

Area of square can be calculated as (side)²

We are given that the side of the square is 14 cm, therefore:

area of square = (14)² = 196 cm²

2- getting the area of the 4 quadrants of the circles:

We know that the 4 drawn circles have equal areas

Therefore:

Total area of 4 quadrants = 4 * area of one quadrant

For one circle:

radius = 14/2 = 7 cm

area of one quadrant = $\frac{1}{4}\pi r^{2}$

Total area of 4 quadrants = $4*\frac{1}{4}\pi r^{2} = \pi (7)^2 = 49\pi = 153.9 = 154$ cm²

3- getting remaining area of square:

remaining area of square = 194 - 154 = 42 cm²

Hope this helps :)

Answer 2

Answer:

42 cm²

Step-by-step explanation:

I have attached the answer. Here I will give you the explanation!

First is entry the given values under appropriate headings, so it will be easy for you.

Next the value of radius is not given, but the question says that the side of square is equal to 14 cm & they gave the circles touch externally on the side of square. So the value of radius is 7cm.

Then they asked the area of shaded one.

So you need to subtract the area of quadrant from the area of square.

And you need to substitute the values given in the beginning down.

If the question gives you the value of pi then use it, otherwise you 22/7

Then calculate as given in the attachment you will get the answer as 42 cm².

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Hope you enjoy!!