Final answer:
The area of the unshaded part of the square ABCF, which consists of a square and a semicircular shaded region, is 98 - 1/2π cm². The calculation involves finding the area of half of the square and then subtracting the area of the semicircle.
Step-by-step explanation:
To find the area of the unshaded part of the figure in the geometry problem pertaining to the square ABCF with a side length of 14 cm, we'll start by calculating the area of the square:
Area of a square = side × side = 14 cm × 14 cm = 196 cm².
Since point E is the center of the square, DE is equal to half the length of the side of the square, which is 7 cm. DF and DC are equal, forming two congruent right-angle triangles, DEF and DEC. Hence, triangle DEF is half of the square whose area is 98 cm².
The shaded region is a semicircle with radius 7 cm. The area of a semicircle is given by (1/2) π r², substituting the radius (7 cm) we get:
Area of a semicircle = 1/2 × π × 7 cm × 7 cm
= 1/2 × π × 49 cm²
= (1/2) × 49π cm²
= 24.5π cm².
Subtract the area of the semicircle from the area of half of the square to get the area of the unshaded part:
Area of the unshaded part = 98 cm² - 24.5π cm²
= 98 cm² - (1/2)π×49 cm²
= 98 - (1/2)π cm².
Thus, the correct answer is (b) 98 - 1/2π.