DIAGRAM IN PICTURE

Mathematics

1 answer:

Marrrta [24]3 years ago

8 0

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

a = h
b = 3
c = 8

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".

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