The Vertices of a triangle are determined by the intersections of the x-axis,y=x,4x+5y=15.

How do I find the area of this particular triangle?
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15 Answers

in general you need to get the three intersecting points and calculate the side length of each side.

in this case, it's a little special that one side lies with x-axis and y=x intersects it at (0,0) so you can find the other two intersecting points easily

by sovling y=x 4x+5y = 15 => (x = 5/3, y = 5/3)

and y = 0 4x+5y=15 (x = 15/4, y = 0)

from this you know the base of the triangle is 15/4 and height is 5/3

so you can easily apply the basexheight/2 formula
by Level 3 User (2.1k points)
Find the length of each of the lines, add them together and find the perimeter. Then, using "s" to represent half the perimeter, you use the formula:
√((s)(s-a)(s-b)(s-c))=A

where A is the area.

This formula is called Heron's Formula and you should look at it if you want a proof.
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