# A triangle has its corners located at the points (x,y) = (6.00,15.00), (x,y) = (11.00,8.00) and (x,y) = (0,0). ?

A triangle has its corners located at the points (x,y) = (6.00,15.00), (x,y) = (11.00,8.00) and (x,y) = (0,0). The coordinates are given in cm. Calculate the area of the triangle.

Can someone help me with this? I keep getting 28.5. I'm not sure what I'm doing wrong

Relevance
• The area

=

0.5| 0....0...1..|

.....|11...8...1..|

.....|..6..15..1..|

=

0.5(11*15-6*8)

=

0.5(117)

=

58.5 cm^2

• A(6,15), B(11,8), C(0,0). Linear units are cm. We shall be using Heron's formula.

a = BC = [(0-11)^2+(0-8)^2]^(1/2)  = rt(121+64) = rt185.stoA = 13.60147051;b = AC = [(0-6)^2)+(0-15)^2]^(1/2) = rt(36+225) = rt261.stoB = 16.15549442;c = AB = [(11-6)^2+(8-15)^2]^(1/2) = rt(25+49)   = rt74.stoC...=   8.602325267;s = (1/2)(a+b+c) =stoD = 19.17964510;(s-a) stoE =   5.578174590(s-b) stoF =   3.024150677(s-c) stoG= 10.57731983s(s-a)(s-b)(s-c)stoH = D*E*F*GstoH = 3422.25.;H^(1/2)stoI = 58.5 (cm)^2.

• get the lengths of the sides.

a = √(5² + 7²) = √74

b = √(6² + 15²) = √261

c = √(11² + 8²) = √185

plug those into

A = √[s(s–a)(s–b)(s–c)]

where s = (a+b+c)/2

I'll let you do the math.

distance between two pointsd = √(Δx² + Δy²)A = √[s(s–a)(s–b)(s–c)]  where s = (a+b+c)/2  a,b,c are the sides of the triangle

• Graph it on paper.

Block out the entire rectangle. The area of interest is the total area - the area of the other three triangles.

total area is 11*15=165 squares.

A is upper left tri=(0,0) to (0,15) to (11,15)

area A = 1/2(15*3)=45

Area B Is upper right =5*7/2=17.5

Area C is lower right=11*8/2=44

A=165-(45+44+17.5)=165-106.5=58.5 sq units

• Find lengths of each side.

Then,   use

Heron's Formula

Area = sqrt( s(s-a)(s-b)(s-c) )

where s = (a+b+c)/2

From (0,0)

length = sqrt(36 + 15^2) = 16.15549442

length = sqrt( 8^2 + 11^2) =  13.60147051

3rd length = sqrt( (11-6)^2 + (8-15)^2)  = 8.602325267

S =  ( 16.15549442 + 13.60147051 + 8.602325267 ) /2

S = 19.1796451

Now, use heron's formula

area = sqrt ( 19.1796451 * (19.179645-1 6.15549442 )*

(19.1796451-13.60147051 ) *(19.1796451- 8.602325267 )

area =sqrt( 21336.5956  )    =58.5   square units

so you are wrong unless it's a typo.