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# Identify and calculate the area and perimeter for triangle, a=8.1mm, b= 4.5mm, c=9.27mm

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Simple maths
to get the perimeter simply add a + b + c
to get area the formula , 1/2 base by perpendicular height

Posted on May 04, 2017

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### Regular pentagon QRSTU has a side length of 12 cm and an area of about 248 square cm. Regular pentagon VWXYZ has a perimeter of 140 cm. Find the area of VWXYZ. Round to the nearest tenth.

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Since you have the coordinates of the three vertices, the most straightforward method is to calculate the length of the sides using the distance formula
d(P_1,P_2)=SQRT((X_1-X_2)^2+(Y_1-Y_2)^2)
where SQRT is the square root function, X_1, Y_1) are the coordinates of point P_1, etc.
With the three lengths available, use Heron's (sometimes called Hero's) to find the area.
Here is Heron's formula.
Let's call the lengths a, b, and c
Let p be the semi-perimeter p= (a+b+c)/2
Then
Area= SQRT [ p(p-a)(p-b)(p-c) ]
Make sure that there is a matching ) parenthesis to the one in the SQRT.

Alternatively,
You can choose the base as the side opposite the vertex (0,0)
Calculate the equation of the line that supports the base.
Calculate the equation of the line issuing from (0,0) and perpendicular t the base.
Calculate the coordinates of the intersection point , call it H, of the base and its perpendicular line (coming from (0,0)).
Calculate the distance OH, that is the height relative to the chosen base.
Use the formula Area= base*height/2

Now it is up to you to choose one of the two methods and calculate the area of that triangle. The second method involves more calculations than the first, and more possibilities of errors. Good Luck

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d(P_1,P_2)=SQRT((X_1-X_2)^2+(Y_1-Y_2)^2)
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Let's call the lengths a, b, and c

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The classic one:
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Heron's Formula if you have the length of the three sides. Let those measures be a, b, and c.
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Hello,
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