find the perimeter and area of this figure.\nround your answer to the nearest hundredth.

Explanation:

Step1: Find the lengths of the sides

• The vertical side: The (y -)coordinates of the two endpoints are (y_1 = 3) and (y_2=7). Using the distance formula for vertical points (d=\vert y_2 - y_1\vert), we get (d_1=\vert7 - 3\vert=4) units.
• The horizontal side: The (x -)coordinates of the two endpoints are (x_1 = 3) and (x_2 = 7). Using the distance formula for horizontal points (d=\vert x_2 - x_1\vert), we get (d_2=\vert7 - 3\vert = 4) units.
• The hypotenuse: Using the Pythagorean theorem (c=\sqrt{a^{2}+b^{2}}), where (a = 4) and (b = 4). So (c=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}\approx5.66) units.

Step2: Calculate the perimeter

The perimeter (P) of a triangle is (P=a + b + c). Substituting (a = 4), (b = 4), and (c\approx5.66), we get (P=4 + 4+5.66=13.66) units.

Step3: Calculate the area

The area (A) of a right - triangle is (A=\frac{1}{2}\times base\times height). Here, base (b = 4) and height (h = 4). So (A=\frac{1}{2}\times4\times4 = 8) square units.

Answer:

(P = 13.66) units, (A=8) units(^{2})