Question

lesson 3 assignment continued calculate the area of the shaded region in each figure. use 3.14 for π and round to the nearest hundredth, if necessary. a) 10 cm 2.5 cm 10 cm b) 3 cm 5 cm 4 cm c) 12 cm 3 cm 3 cm d) 4 cm 8 cm stretch optional 1 determine the area of the shaded region. all circles have the same radius. 10 in.

Explanation:

a.

Step1: Find area of square

The area formula for a square is $A_{square}=s^2$, where $s = 10$ cm. So $A_{square}=10^2=100$ $cm^2$.

Step2: Find area of circle

The area formula for a circle is $A_{circle}=\pi r^2$, with $r = 2.5$ cm. So $A_{circle}=3.14\times2.5^2=3.14\times6.25 = 19.625$ $cm^2$.

Step3: Find area of shaded region

$A = A_{square}-A_{circle}=100 - 19.625=80.375\approx80.38$ $cm^2$.

Step1: Find area of circle

The diameter of the circle is the diagonal of the rectangle. Using the Pythagorean theorem for the rectangle with sides $3$ cm and $4$ cm, the diagonal $d=\sqrt{3^2 + 4^2}=5$ cm, so the radius $r=\frac{5}{2}=2.5$ cm. Then $A_{circle}=3.14\times2.5^2=19.625$ $cm^2$.

Step2: Find area of rectangle

The area of the rectangle is $A_{rectangle}=3\times4 = 12$ $cm^2$.

Step3: Find area of shaded region

$A=A_{circle}-A_{rectangle}=19.625 - 12=7.625\approx7.63$ $cm^2$.

Step1: Find area of rectangle

The area of the rectangle is $A_{rectangle}=12\times(3 + 3+3)=12\times9 = 108$ $cm^2$.

Step2: Find area of two circles

The area of one - circle is $A_{circle}=\pi r^2$ with $r = 3$ cm. So the area of two circles is $2\times3.14\times3^2=2\times3.14\times9=56.52$ $cm^2$.

Step3: Find area of shaded region

$A=A_{rectangle}-A_{two - circles}=108 - 56.52 = 51.48$ $cm^2$.

Answer:

$80.38$ $cm^2$

b.