Let's take a look at the given diagram. Notice that in an isosceles trapezoid the legs l are congruent.
Since we are given that the perimeter of the figure is 44 units, we can write and solve equation for l.
20+ l+ l+ 4= 44
Let's solve the above equation.
The leg length is 10 units. Next let's draw the heights h of the trapezoid. Notice that these heights divide the trapezoid into two congruentright triangles and a rectangle.
Next, if we call the length of the second leg of each triangle x, then we can see that two times x plus 4 is equal to 20.
2 x+ 4= 20 ⇒ x=8
Let's add this information to our diagram.
Now notice that we can evaluate h using the Pythagorean Theorem. According to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
Notice that since h represents the height, we considered only positive cases when taking a square root of h^2.
Now we have all the information we need to evaluate the area of the trapezoid. Let's recall the formula for this area.
A=1/2h(b_1+b_2)
Finally, let's substitute the height and both bases of our triangle into the above formula.
