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ABC is an isosceles triangle.
Calculate the perpendicular height. (h)
Hence calculate the area of the triangle.

Answers:  

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

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.

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

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".

answer: approximately 206 bones

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