Question

find the perimeter and area of this figure. p = ? units a = units²

Explanation:

Step1: Find the lengths of the sides

• Horizontal side: The horizontal side goes from $x = 2$ to $x = 8$, so its length is $8 - 2=6$ units.
• Vertical side: The vertical side goes from $y = 1$ to $y = 9$, so its length is $9 - 1 = 8$ units.
• Slanted side: Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, for the points $(2,9)$ and $(8,1)$:

$$d=\sqrt{(8 - 2)^2+(1 - 9)^2}=\sqrt{6^2+(- 8)^2}=\sqrt{36 + 64}=\sqrt{100}=10$$ units.

Step2: Calculate the perimeter

Perimeter $P$ is the sum of all sides. So $P=6 + 8+10=24$ units.

Step3: Calculate the area

The figure is a right - triangle. Area of a triangle $A=\frac{1}{2}\times base\times height$. Here, base $b = 6$ units and height $h = 8$ units. So $A=\frac{1}{2}\times6\times8 = 28$ units².

Answer:

$P = 24$ units, $A = 28$ units²