We are given the perimeter and the lengths of the bases of an isosceles trapezoid, and are asked to evaluate its area. Let's take a look at the given diagram. We will call the legs of this trapezoid l.
Our first step will be to find the value of l using the fact that the perimeter of this trapezoid is 74 meters. Recall that the perimeter of a figure is the sum of its all sides.
74= 19+l+l+ 35
Let's solve the above equation for l.
Each leg in this trapezoid has a length of 10 meters. Now, to find the area of a trapezoid we need to find its height. We will call it h. Remember that height is always perpendicular to the longer base.
As we can see, the heights divide our trapezoid into one rectangle and two congruent right triangles. If we call the missing legs of these triangles x we can see that two times x plus 19 is equal to 35.
Now we can write and solve the equation we described above.
Now we can solve for h using the Pythagorean Theorem. According to this theorem the sum of squared legs of a right triangle is equal to its squared hypotenuse.
10^2=8^2+ h^2
Let's solve the above equation. Notice that since h represents the height we will consider only the positive case when taking the square root of h^2.
