SOLUTION: The congruent sides of an isosceles triangle measure 6cm, and the base measures 8cm. What is the area? I don't understand how you would find the necessary height of the triangle, o

Question 573316: The congruent sides of an isosceles triangle measure 6cm, and the base measures 8cm. What is the area? I don't understand how you would find the necessary height of the triangle, or how the base of an isosceles triangle can be longer than the two other congruent sides. Thank you:).
Found 3 solutions by scott8148, stanbon, lwsshak3:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
the altitude (height) bisects the base and forms two congruent right triangles

by Pythagoras ___ h^2 + (b / 2)^2 = 6^2
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The congruent sides of an isosceles triangle measure 6cm, and the base measures 8cm. What is the area? I don't understand how you would find the necessary height of the triangle, or how the base of an isosceles triangle can be longer than the two other congruent sides. Thank you:).
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Draw the base = 8 cm
Draw the 2 sides; each = 6 cm
Draw a perpendicular bisector of the base (that is the height of the triangle).
Use Pythagoras to find the height
6^2 = 3^2 + h^2
36 = 9 + h^2
h^2 = 27
h = 3sqrt(3)
-----
Area = (1/2) base*height
Area = (1/2)6*3sqrt(3)
Area = 9sqrt(3) sq. cm.
===========================
Cheers,
Stan H.
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Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
The congruent sides of an isosceles triangle measure 6cm, and the base measures 8cm. What is the area? I don't understand how you would find the necessary height of the triangle, or how the base of an isosceles triangle can be longer than the two other congruent sides.
**
Just imagine a flattened isosceles triangle and you can see that the base can be longer than the sides. Draw a line from the apex perpendicular to the base. You now will be working with a right triangle where the hypotenuse is one of the sides (6cm), one of the legs is half of the base (4), and the other leg is the height (h).
..
h^2=6^2-4^2
h^2=36-16=20
h=√20
Area=1/2 base*height
=1/2*8*√20
=4√20=16√5
ans:
Area=16√5 cm^2
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