Answers:
- h = sqrt(55) centimeters
- area = 3*sqrt(55) square cm
Your teacher may want the numbers only, so you may have to leave off the units.
We have these approximations:
sqrt(55) = 7.416198
3*sqrt(55) = 22.248595
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Explanation:
ABC is isosceles, meaning that the altitude (aka height) h cuts side BC into two equal pieces. BC = 6 cuts in half to 3.
Let's say point D is on BC and at the base of the altitude. In other words, D is at the midpoint. Triangle ABC is cut into two smaller triangles ABD and ADC.
Let's focus on triangle ADC, which is a right triangle. It has a horizontal side of DC = 3 and vertical side AD = h. The hypotenuse is AC = 8.
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Let
Apply the pythagorean theorem
a^2 + b^2 = c^2
h^2 + 3^2 = 8^2
h^2 + 9 = 64
h^2 = 64-9
h^2 = 55
h = sqrt(55) ..... exact
h = 7.416198 ..... approximate
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Once we determine the height of triangle ABC, we can compute the area
base = BC = 6 cm
height = AD = h = sqrt(55) cm
area = 0.5*base*height
area = 0.5*6*sqrt(55)
area = 3*sqrt(55) .... exact
area = 22.248595 .... approximate
The units for the area are "square cm" or "cm^2".
