Answer:
(a) square: 196 cm²
(b) circle: 153.94 cm²
(c) corners: 42.06 cm²
Step-by-step explanation:
You want the area of a square that has sides of length 14 cm, the area of the inscribed circle, and the difference.
(a) Square
The area of the square is the square of its side lengths:
A = s² = (14 cm)² = 196 cm²
The area of the square is 196 cm².
(b) Circle
In terms of the diameter, the area of a circle is ...
A = π(d/2)² = (π/4)d²
The diameter is the same length as the side of the square, so this is π/4 times the area of the square.
A = (π/4)(196 cm²) ≈ 153.94 cm²
The circle area is about 153.94 cm².
(c) Blue
The area of the blue sections is the difference between the area of the square and the area of the circle:
A = 196 cm² -153.94 cm² = 42.06 cm²
The blue area is about 42.06 cm².
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Additional comment
The use of 3.14 for π will give an answer accurate to 2 or 3 significant figures. The "pi button" will give an answer accurate to calculator precision. Here, we want answers with 4 or 5 significant figures, so we prefer to use the "pi button" value for π.
It can be handy to remember that the fraction of a rectangle taken up by an inscribed circle, semicircle, or quarter-circle is π/4 of the rectangle area.
