Four equal circles are drawn with the vertices of a square as their centres. The side of the square is 7 cm. Each circle has radius 3.5 cm (half the side), so that the arc from each vertex reaches the midpoint of each adjacent side. Find the total area (in sq cm) of the parts of these circles that lie outside the square (assume pi = 22/7).

Introduction / Context:
This is a geometry “composite area” problem involving circles and a square. With a circle centred at each vertex, only one quadrant of each circle lies inside the square (the quadrant in the corner). The remaining three quadrants of each circle lie outside the square. Since there are four circles, the total area outside the square equals 4*(3/4 of one circle area) = 3*(one circle area). The key is recognizing the quadrant relationship and using the correct radius (half the side).

Given Data / Assumptions:

• Square side = 7 cm
• Circle centres are the four vertices
• Radius r = 3.5 cm (half of 7 cm)
• Area of circle = pi*r^2
• Inside square: 1 quadrant per circle

Concept / Approach:
For each vertex-centred circle, the portion inside the square is a 90 degree sector (a quadrant). So area outside square for one circle = (3/4)*pi*r^2. For four circles: total outside = 4*(3/4)*pi*r^2 = 3*pi*r^2. Then substitute r = 3.5 and pi = 22/7.

Step-by-Step Solution:
Radius r = 3.5 cmArea of one full circle = pi*r^2 = pi*(3.5^2) = pi*12.25Area of one quadrant (inside square) = (1/4)*pi*12.25Area outside square for one circle = (3/4)*pi*12.25Total outside for four circles = 4*(3/4)*pi*12.25 = 3*pi*12.25Using pi = 22/7: total = 3*(22/7)*12.2512.25 = 49/4, so total = 3*(22/7)*(49/4) = 3*(22*7/4) = 3*(154/4) = 3*38.5 = 115.5 sq cm

Verification / Alternative check:
Another quick check: one circle area = (22/7)*12.25 = (22/7)*(49/4) = 38.5. Total outside should be 3 times that = 115.5, matching the computed result exactly with pi = 22/7.

Why Other Options Are Wrong:
Values near 104 or 111 usually come from using pi = 3.14 or rounding too early. 119.21 can appear if the radius is taken as 7 instead of 3.5 or if area outside is miscounted. 98.00 indicates an incorrect fraction of the circle used (such as 1/2 instead of 3/4).

Common Pitfalls:
Assuming radius equals the side (7) instead of half (3.5). Counting area inside square incorrectly (it is exactly one quadrant per circle). Mixing up “outside square” with “outside all circles.” Using an inconsistent value of pi compared to the options basis.

Final Answer:
115.50 sq cm