I already know the perimeter but I keep getting different answers for the area.Help me,this is due in no time!

Question

Use the Pythagorean theorem to show that the given points are the vertices of a right triangle. (Do this on paper. Your teacher may ask you to turn in this work.) Find the area, A, and the perimeter, P, of the triangle. Give your answers correct to 2 decimal places.
(3, 10), (-1, 2), (9, -3)
perimeter is 34.44

Answer 1

area = 1/2 base * height

Your base and height are the two segments joining (3,10)-(-1,2) and (-1,2)-(9,-3).

So, use the distance formula to get the lengths of these two segments:

segment 1 = SQRT[(3-(-1))^2 + (10-2)^2]

= SQRT (16 + 64) = SQRT(80) = 4*SQRT(5)

segment 2 = SQRT[(9-(-1))^2 + (-3-2)^2]

= SQRT (100 + 25) = SQRT(125) = 5*SQRT(5)

so, 1/2 * base * height =
1/2 * 4SQRT(5) * 5SQRT(5) =
1/2 * 4 * 5 * 5 = 50

So the area of your triangle is 50

HTH! :-)

Answer 2

actually half of the problem you have solved. if you have calculated length of sides by using distance formula(because you have found perimeter so i assume you know measurements of sides)
now you have to prove that its a right angled triangle for that prove square of greatest side is equal to sum of squares of remaining two sides.
to find area use formula(A)=1/2 X BASEXHEIGHT
here base and height will be sides including right angle. hope this will help.
for better help use pen tablet.