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(25points) Which of the following is the ratio of the area of the shaded region to the total area of the square
a)1/2
b)1/3
c)3/8
d)3/4


25points Which Of The Following Is The Ratio Of The Area Of The Shaded Region To The Total Area Of The Square A12 B13 C38 D34 class=

Sagot :

Answer:

C

Step-by-step explanation:

We want to find ratio of the area of the shaded region to the total area of the square.

First, we can find the total area of the square. Since QR = 7, each side of the square measures 7. Therefore, its area is:

[tex]A=(7)^2=49\text{ units}^2[/tex]

Instead of finding the shaded area, we can find the areas that are not shaded. Subtracting that into the total area will then give us the shaded area.

QRP is a triangle. Since PQRS is a square, QR = 7 = RS = SP = PQ.

So, the area of ΔQRP is:

[tex]\displaystyle A_{\Delta QRP}=\frac{1}{2}(7)(7)=24.5[/tex]

UTS is also a triangle. We are given that RU = US and PT = TS. So, Points U and T bisect RS and SP, respectively. Since RS = SP = 7, RU = US = PT = TS = 3.5. So, the area of ΔUTS is:

[tex]\displaystyle A_{\Delta UTS}=\frac{1}{2}(3.5)(3.5)=6.125[/tex]

Therefore, the total area of the white region is:

[tex]A_{\text{white}}=6.125+24.5=30.625[/tex]

Thus, the shaded region is:

[tex]A_{\text{shaded}}=49-30.625=18.375[/tex]

Then the ratio of the shaded region to the total area of the square will be:

[tex]\displaystyle R_{\text{shaded:total}}=\frac{18.375}{49}=\frac{3}{8}[/tex]

Our answer is C.