Altered Square

The original perimeter of the square was $4 \cdot 26 = 104.$ Let's see how it has changed.

Four segments of length $26-18 = 8$ have been removed, for a total of 32 units removed. On the other hand, 2 quarter-circle arcs have been added. Since the circumference of an entire circle with radius 8 is $2\cdot 8 \cdot \pi = 16\pi,$ 2 quarter-circles will have length $8\pi.$

Thus, the perimeter is $\underbrace{104}_{\text{original square}} - \underbrace{32}_{\text{parts of square missing}} + \underbrace{8\pi}_{\text{new curved length}} = 72 + 8\pi.$

Radius of circle = 26 -18 = 8

2 quarter circle's circumference = $2 \times \pi \times 8 \times \frac{1}{2}= 8\pi$

Perimeter = $18 \times 4 + 8\pi.$

The radius of the circle=26-18=8.So the arc of the quarter circles is=(2* pi* r)/4=(pi * r)/2=3.1416 * 8)/2=12.5664.There are two of it so 2 *12.5664=25.1328.Now every straight line is 18,so 4 of them makes the summation (4 *18)=72.So the perimeter of the shape=25.1328+72=97.1328=97.133

As said there are 2 quarter circles in the square.

Radius of circles would be 26 - 18 = 8.

As it is quarter circle there will be angle of 90 degree.

Hence arc length will be as follows.

arc = (θ × π/180) × r = 90 * π/180 * 8 = 12.56637

Perimeter will be 18 + 18 + 18 + 18 + 12.56637 + 12.56637 = 97.13274.

It is actually a square of each side 26. after cutting its 2 corners in quarter circular shape of radios 8 (26-18=8=r). we get the length of the circular path is (1/4) (2πr) => (1/2) πr ; and the sum of the length of the circular paths is (1/2) πr + (1/2) πr = πr = π* 8 . now the straight lines are of 18, and there four straight lines so its total length is 4* 18=72 and the total length or the perimeter of the shape is 72+π* 8= 97.133

the radius of all the quarter circles is 8/2=4.Now find the perimeter of each as 4*pi/2=2pi.As there are 4 equal quarter circles and 4 sides of 26-8=18. calculate peri. by 4(2pi+18)=97.133

From giveen details,radius of circle is 8. Perimeter full circle is 2 piX8 for two quarter circles it will be 25 .33.for rest of square prtion it is 4 X18 =72. adding all above perimeter of the diagram is 97.33 Ans. K.K.GARG,India

Radius of circle(r) = 26 - 18 = 8

Perimeter of 2 quarter circle (p)= 2 x (1/4) x 2 x pi x r = 8xpi

Perimeter of the shape = 18x4 + p= 97.133