Question

Two sides of a triangle are equal in length. The base of the triangle (the side that isn't equal in length to the other two) measures `7.6` cm. The two equal sides both measure `5` cm. What is the area of the triangle?

Answer 1

The area is approximately `12.35` square units.

Explanation:

This is an isosceles triangle, so if we were to draw an altitude between where the two equal sides meet and the longer side, the altitude would cut the longer side in half, leaving us with two right-angled triangles of hypotenuse `5` and base `3.8`.

Now, by pythagorean theorem, letting the altitude be `a`, we have

`a^2 + (3.8)^2 = 5^2`

`a = sqrt(10.56)`

We'll keep that as an exact value for now.

The formula for area of a triangle is `A = (b * h)/2`. Therefore:

`A =( sqrt(10.56) * 3.8)/2`

However, we have two of these triangles, so the total area is

`A_"total" = 2(sqrt(10.56) * 3.8)/2 ~~12.35`

Hopefully this helps!

Answer 2

12.35

Explanation:

With two sides of equal length, this is an isosceles triangle. Thus the line from the apex to the base will divide the lower side exactly in half (3.8). Then we can use the equation for the area of a triangle, where the height is calculated from the Pythagorean Theorem.

`5^2 = 3.8^2 + h^2` ; `h^2 = 25 – 14.44` ; `h^2 = 10.56` ; h = 3.25.

`A = (1/2)*b*h` ; `A = (1/2)*7.6*3.25` ; A = 12.35