Answer:
745.4 cm^2
Step-by-step explanation:
The composite figure is made up of a rectangle 25 cm by 20 cm and a semicircle of radius 12.5 cm.
We add the two areas to find the total area.
total area = area of rectangle + area of semicircle
TA = LW + (1/2)(pi)r^2
TA = (25 cm)(20 cm) + (1/2)(3.14159)(12.5 cm)^2
TA = 500 cm^2 + 245.4 cm^2
TA = 745.4 cm^2
Use the Law of Sines:
sin B sin 81 sin 44
---------- = ----------- = --------------
side AC 68 side AB
Then (side AB)(sin 81) = 68(sin 44), or
68 sin 44
side AB = ----------------------- = 47.83 units long
sin 81
1. 20 squared + 48 squared = 2704
square root of 2704 is 52. Answer: 52 inches.
2. -18 squared + 82 squared = 6400
square root of 6400 is 80 Answer: 80 inches
ANSWER
The area of square ABCD is

EXPLANATION
The area of square ABCD is the square of the length of one side.
That is the area of ABCD is |AD|²
From Pythagoras theorem,

We can read from the graph that, each box is one unit.
This implies that,



Therefore the area of square ABCD is 25 square units.
The correct answer is option C.