Number 19 find the area of this isosceles triangle

The formula to find area of a triangle is base * height * 1/2.

With that in mind we know the base, 4.

In order to find the height we cut the triangle in half forming two right triangles.

With a right triangle we can apply the Pythagorean Theorem to find our unknown side.

In this case √21 is our hypotenuse and we use 2 as a side length instead of 4 because we cut the triangle in half. so you'll get something like this:

2^2 + x^2 = √21 ^ 2
Simplify: 4 + x^2 = 21
Subtract 4 from each side: x^2 = 17
Square root both sides: x = √17

Now that we know √17 is the height, multiply out the area formula for a triangle.

√17 * 4 = 4√17, * 1/2 = 2√17