Answer :

kudzordzifrancis

Answer:

Perimeter : 22.81 to the nearest hundredths

Area: 24 square units

Step-by-step explanation:

The vertices of ∆ABC are located at A(-2, 2), B(6, 2), and C(0, 8).

The perimeter is the distance around the figure.

Use the distance formula to find the side lengths of the triangle and add them up.

The distance formula is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]|AB|=\sqrt{(6--2)^2+(2-2)^2}[/tex]

[tex]|AB|=\sqrt{(8)^2+(0)^2}[/tex]

[tex]|AB|=\sqrt{64}=8[/tex] units

[tex]|AC|=\sqrt{(0--2)^2+(8-2)^2}[/tex]

[tex]|AC|=\sqrt{(2)^2+(6)^2}[/tex]

[tex]|AC|=\sqrt{40}=6.32[/tex] units

[tex]|BC|=\sqrt{(0-6)^2+(8-2)^2}[/tex]

[tex]|BC|=\sqrt{(-6)^2+(6)^2}[/tex]

[tex]|BC|=\sqrt{72}=8.49[/tex] units

The perimeter is 8+6.32+8.49=22.81 units

The area of this triangle is given by: [tex]\frac{1}{2}|AB|\times |CD|[/tex] (see attachment)

[tex]Area=\frac{1}{2}\times 8\times 6[/tex]

[tex]Area=24[/tex] square units.

${teks-lihat-gambar} kudzordzifrancis
MrRoyal

The perimeter of the triangle is 22.8 units and the area is 24 square units

The vertices of the triangle are given as:

A(-2, 2), B(6, 2), and C(0, 8).

Calculate the length of each side using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]AB = \sqrt{(-2 -6)^2 + (2 -2)^2} = 8[/tex]

[tex]BC = \sqrt{(6 - 0)^2 + (2 -8)^2} = 8.5[/tex]

[tex]AC = \sqrt{(-2 - 0)^2 + (2 -8)^2} = 6.3[/tex]

The perimeter (P) is then calculated as:

P =AB + BC + AC

So, we have:

P = 8 + 8.5 + 6.3

P = 22.8

The area (A) of the triangle is calculated as:

[tex]A =0.5 * |A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|[/tex]

This gives

[tex]A =0.5 * |-2 (2- 8) + 6(8 - 2) + 0(2 - 2)|[/tex]

[tex]A =0.5 * 48[/tex]

[tex]A = 24[/tex]

Hence, the perimeter of the triangle is 22.8 units and the area is 24 square units

Read more about area and perimeter at:

https://brainly.com/question/17297081

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