Answer:
1. D. \(50\text{ units}^2\)
2. D. 45 units.
Step-by-step explanation:
We have been two graphs.
1. To find the area of our given triangle we will use distance formula.
\(\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Upon substituting coordinates of base line of our triangle we will get,
\(\text{Base length of triangle}=\sqrt{(15-5)^2+(5-15)^2}\)
\(\text{Base length of triangle}=\sqrt{(10)^2+(-10)^2}\)
\(\text{Base length of triangle}=\sqrt{100+100}\)
\(\text{Base length of triangle}=\sqrt{200}\)
\(\text{Base length of triangle}=10\sqrt{2}\)
Now let us find the height of triangle similarly.
\(\text{Height of triangle}=\sqrt{(20-15)^2+(10-5)^2}\)
\(\text{Height of triangle}=\sqrt{(5)^2+(5)^2}\)
\(\text{Height of triangle}=\sqrt{25+25}\)
\(\text{Height of triangle}=\sqrt{50}\)
\(\text{Height of triangle}=5\sqrt{2}\)
\(\text{Area of triangle}=\frac{\text{Base*Height}}{2}\)
\(\text{Area of triangle}=\frac{10\sqrt{2}*5\sqrt{2}}{2}\)
\(\text{Area of triangle}=\frac{50*2}{2}\)
\(\text{Area of triangle}=50\)
Therefore, area of our given triangle is 50 square units and option D is the correct choice.
2. Using distance formula we will find the length of large side of triangle as:
\(\text{Large side of rectangle}=\sqrt{(14-1)^2+(21-8)^2}\)
\(\text{Large side of rectangle}=\sqrt{(13)^2+(13)^2}\)
\(\text{Large side of rectangle}=\sqrt{169+169}\)
\(\text{Large side of rectangle}=\sqrt{338}\)
\(\text{Large side of rectangle}=13\sqrt{2}\)
\(\text{Small side of rectangle}=\sqrt{(4-1)^2+(5-8)^2}\)
\(\text{Small side of rectangle}=\sqrt{(3)^2+(-3)^2}\)
\(\text{Small side of rectangle}=\sqrt{9+9}\)
\(\text{Small side of rectangle}=\sqrt{18}\)
\(\text{Small side of rectangle}=3\sqrt{2}\)
\(\text{Perimeter of rectangle}=2(\text{Length + Width)}\)
\(\text{Perimeter of rectangle}=2(13\sqrt{2}+3\sqrt{2}}\)
\(\text{Perimeter of rectangle}=2(16\sqrt{2}}\)
\(\text{Perimeter of rectangle}=32\sqrt{2}\)
\(\text{Perimeter of rectangle}=45.2548339959390416\approx 45\)
Therefore, the perimeter of our given rectangle is 45 units and option D is the correct choice.
