The following three shapes are based only on squares, semicircles, and quarter circles. find the perimeter and the area of each shaded part. give your answer as a completely simplified exact value in terms of π (no approximations).

Solution:- In the given figure

Side of square= 10 cm

area of square =  side x side m= 10 x 10 = 100 sq cm

Now , diameter of semi circle AOD = 2r = 10cm

⇒ radius of  semi circle AOD = 5 cm

∴ area of AOD =

similarly Area of semicircle BOC =

Area of white portion in figure 1 = area of square - [ area of semicircle BOD + area of semicircle AOD]

=

Total area of white portion in the given figure=

∴Area of Shaded portion = area of square - area of total white portion

=

So the area of shaded portion is

Now perimeter of AD(which is a semicircle) = (as perimeter of semicircle=πr)

So the perimeter of shaded region = 4×perimeter of AD=4×15.7=62.8cm

the least common denominator is 40

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.