4. Not enough info, the shape is cut off. Are there 4 sides or 5? If there's a 5th side, is it slanted or parallel to the one labeled 10 ft?
5. The circle has a radius of 7 m, so its area is
π (7 m)² = 49π m²
Subtract from this the area of the white triangle. It has a base length equal to the diameter (i.e. twice the radius) of the circle, and a height equal to the radius, so its area is
1/2 (14 m) (7 m) = 49 m²
So the area of the shaded region is (49π - 49) m², or 49 (π - 1) m².
6. The rectangle has length 14 yd and height equal to the diameter of the circular cutout, 10 yd, so its area is
(14 yd) (10 yd) = 140 yd²
The circular cutout is a semicircle with radius 5 yd, so its area is
1/2 π (5 yd)² = 25π/2 yd²
Then the area of the shaded region is (140 - 25π/2) yd², or 1/2 (280 - 25π) yd².
7. The circle has radius 13 in, so its area is
π (13 in)² = 169π in²
The triangle has height 23 in and length 12 in, so its area is
1/2 (23 in) (12 in) = 138 in²
Then the area of the shaded region is (169π - 138) in².
8. The shaded region is a rectangle with a smaller rectangular cutout. The larger rectangle has height 19 cm and length 18 cm + 16 cm = 34 cm, so its area is
(19 cm) (34 cm) = 646 cm²
The smaller rectangular cutout has length 16 cm and height 19 cm - 16 cm = 3 cm, so its area is
(16 cm) (3 cm) = 48 cm²
Then the area of the shaded region is 646 cm² - 48 cm² = 598 cm².
9. The semicircular piece has radius 3 m, so its area is
1/2 π (3 m)² = 9π/2 m²
The triangle has height equal to the semicircle's diameter, 6 m, and length 9 m, so its area is
1/2 (6 m) (9 m) = 27 m²
Then the area of the shaded region is (9π/2 + 27) m², or 1/2 (9π + 54) m².
