Question

a wire is bent to make the shape below. The shape is made up of four identical circles. each circle intersects two other circles. The four circled meet at a common point T, which is the center of square PQRS. Find the length of the wire. Find the area of the whole shape.

Answer 1

1. Length of the wire = perimeter of the square = 112 cm

2. Area of the whole shape = 4[1/2(area of circle)] + area of the square = 2,014.88 cm².

What is the Area of a Circle?

Area of a circle = πr²

1. The length of the wire = perimeter of the square = 4(28)

Perimeter of the square = 112 cm

2. Area of the whole shape = 4[1/2(area of circle)] + area of the square

= 4[1/2(πr²)] + s²

Given the following:

• r = 1/2(28) = 14 cm
• s = 28 cm
• π = 3.14

Plug in the values into the equation:

Area of the whole shape = 4[1/2(area of circle)] + area of the square

= 4[1/2(3.14 × 14²)] + 28²

= 2,014.88 cm².

Therefore, the area of the whole shape = 4[1/2(area of circle)] + area of the square = 2,014.88 cm².

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