SOLUTION: 1. Find the area of an equilateral triangle if each side measures 12 cm. A.24 cm^2 B.36 cm^2 C.24√3 cm^2 D.36√3 cm^2 E.40√2 cm^2 2. Find the area of an is

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: 1. Find the area of an equilateral triangle if each side measures 12 cm. A.24 cm^2 B.36 cm^2 C.24√3 cm^2 D.36√3 cm^2 E.40√2 cm^2 2. Find the area of an is      Log On

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Question 921447: 1. Find the area of an equilateral triangle if each side measures 12 cm.
A.24 cm^2
B.36 cm^2
C.24√3 cm^2
D.36√3 cm^2
E.40√2 cm^2
2. Find the area of an isosceles triangle if the measure of the congruent sides is 10 cm each and the altitude is 8 cm.
A.12 cm^2
B.24 cm^2
C.24 cm^2
D.48 cm^2
E.54 cm^2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1. Here is the triangle ( green%28h%29= height in centimeters):
6%5E2%2Bh%5E2=12%5E2 according to the Pythagorean theorem
6%5E2%2Bh%5E2=12%5E2 ---> 36%2Bh%5E2=144 ---> h%5E2=144-36 ---> h%5E2=108 ---> h=sqrt%28108%29 ---> h=sqrt%2836%2A3%29 ---> h=sqrt%2836%29%2Asqrt%283%29 ---> h=6sqrt%283%29
The area of a triangle is calculated as area=%281%2F2%29%2Abase%2Aheight , so for this triangle
area=%281%2F2%29%2A12%2A6sqrt%283%29 ---> highlight%28area=36sqrt%283%29%29 square centimeters.

2. Here is the triangle ( x= length of half of the base, in cm):
x%5E2%2B8%5E2=10%5E2 according to the Pythagorean theorem
x%5E2%2B8%5E2=10%5E2 ---> x%5E2%2B64=100 ---> x%5E2=36 ---> x=sqrt%2836%29 ---> x=6 ,
so the base of the triangle measures 2%2A6cm=12cm
The area of a triangle is calculated as area=%281%2F2%29%2Abase%2Aheight , so for this triangle
area=%281%2F2%29%2A12%2A8 ---> highlight%28area=48%29 square centimeters.