Answer:
The perimeter is 20.9 cm and the area is 16 cm squared.
Step-by-step explanation:
Perimeter and Area
Perimeter
Perimeter is the sum of the side lengths of a given 2-D shape.
Area
Area quantifies the space that the 2-D shape takes up by utilizing its side lengths.
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Solving the Problem
Perimeter
We can easily find the lengths of line AC and AB since they're straight lines that are parallel to an axis.
Simply counting the units from A to C and A to B respectively or, --taking the difference of line AC's y values and the difference of line AB's x values--, we can tell that two side lengths of the triangle are 8 and 4 units.
To find the length of BC, which is diagonal, we can use distance formula to find its length.
[tex]BC=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} =\sqrt{(4-0)^2+(9-1)^2}\\\\=\sqrt{16+64} =\sqrt{80} \\\\\Longrightarrow BC=4\sqrt{5}\\[/tex]
Adding all the side lengths up, the perimeter is
[tex]8+4+4\sqrt{5}=12+4\sqrt{5}=20.944[/tex].
Area
We found the lengths of AC and AB from earlier, which happens to be the base and height of the triangle.
Plugging their values into the area formula for a triangle we get,
[tex]A=\dfrac{1}{2} bh=\dfrac{1}{2} (4)(8)=16[/tex].
