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katrin [286]
3 years ago
6

The vertices of triangle PQR are listed below.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
5 0

Answer:

A. 32 units

Step-by-step explanation:

First, we need to find all of the side lengths of triangle using distance formula:

  • Distance = \sqrt{(x2-x1)^2 + (y2-y1)^2}

Now, we can calculate length of PQ, QR and PR sides by using their vertices and above formula:

  • PQ=\sqrt{(-13-(-5))^2+(-3-3)^2} =\sqrt{8^2+6^2}=10
  • QR=\sqrt{(-5-(-13))^2+(-9-(-3))^2} =\sqrt{8^2+6^2}=10
  • PR=\sqrt{(-5-(-5))^2+(-9-3)^2} =\sqrt{0^2+12^2}=12

For perimeter we add up the length of all of its sides:

  • Perimeter = PQ +QR + PR=10+10+12=32

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Answer:

Area of the garden:

\begin{equation*} 398.93\text{ ft}^2 \end{equation*}

Explanation:

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Let's now go ahead and determine the area of the semicircle using the below formula;

A_{sc}=\frac{\pi r^2}{2}=\frac{3.14*\left(7\right)^2}{2}=\frac{3.14*49}{2}=\frac{153.86}{2}=76.93\text{ ft}^2

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We can now determine the area of the garden by adding the area of the semicircle and that of the rectangle together;

\begin{gathered} Area\text{ of the garden = Area of semi circle + Area of rectangle } \\ =76.93+322 \\ =398.93\text{ ft}^2 \end{gathered}

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