16.8k views
5 votes
HELP PLEASE 10 POINTS SHOW YOUR WORK

HELP PLEASE 10 POINTS SHOW YOUR WORK-example-1

1 Answer

2 votes

1. The overall size of the shape is 9 cm high by (8+6) = 14 cm wide. The cutout in the upper right corner has a depth of (9-6) = 3 cm. The shaded area is that of a 9×14 rectangle with a 3×6 rectangle subtracted.

... (9 cm)×(14 cm) - (3 cm)×(6 cm) = 126 cm² -18 cm² = 108 cm²

2. The area is that of a semicircle with 5 m radius added to a right triangle with legs 10 m and 15 m.

The area of a whole circle is given by

... A = πr²

so the area of your semicircle is

... A = (1/2)π(5 m)² = 12.5π m² ≈ 39 m²

The area of the triangle is

... A = (1/2)bh = (1/2)(15 m)(10 m) = 75 m²

Then the shaded area is

... 39 m² +75 m² = 114 m²

3. This is a 14 m × 24.5 m rectangle with a 7 m square cutout. Its area is ...

... (14 m)×(24.5 m) - (7 m)×(7 m) = 343 m² -49 m² = 294 m²

4. The geometry shown is impossible, but we'll assume the intent is to subtract the area of a circle with 4 inch radius from that of a triangle of width and height 12 inches. Using the above formulas, the shaded area will be

... A = (1/2)bh - πr² = (1/2)(12 in)(12 in) - π(4 in)² = 72 in² -16π in² ≈ 22 in²

_____

The attached figure shows why the geometry of problem 4 is impossible. An 8-inch circle will not fit in the triangle in the way it is shown in the figure.

HELP PLEASE 10 POINTS SHOW YOUR WORK-example-1