Question

2.

What is the area of a triangle whose vertices are J(-2,1), K(4,3), and L(-2,-5) ?
(7 points)
a. What is the formula for the area of the triangle?
b.
Find the length of the base. Do not round to a decimal.
C.
Find the length of the height. Do not round to a decimal.
d. Find the area of the triangle.

Answer 1

Area: T = 18

a. The triangle area using Heron's formula: T= sqrt(s(s−a)(s−b)(s−c) )

​b. 2
`√(10)`

c. h = 5.69

d. T = 18

Explanation:

a. T= sqrt(s(s−a)(s−b)(s−c) )

T=sqrt( 11.16(11.16−10)(11.16−6)(11.16−6.32) )

​T= sqrt(324 )

​T =18

b. We compute the base from coordinates using the Pythagorean theorem

c= sqrt( ((−2−4)^2)+ ((1−3) ^2) )

c= sqrt(40) = 2sqrt(10)

c. Calculate the heights of the triangle from its area

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