The formula for the area of a trapezoid is A= 12h(b_1+b_2). Does the diagram provide all of the necessary information?
52sqrt(3)
Practice makes perfect
The area of a trapezoid is half the product of its height and the sum of its bases.
A= 12h(b_1+b_2)
To find the area of the given trapezoid, we first need to find the length of its height h and its minor base b. To do so, let's draw an altitude that divides the trapezoid into a right triangle and a rectangle.
We have a 30^(∘)-60^(∘)-90^(∘) triangle. In this type of triangle the length of the shorter leg is half the length of the hypotenuse. Moreover, the length of the longer leg is sqrt(3) times the length of the shorter leg. With this information and knowing that the length of the hypotenuse is 8 feet, we can find the length of both legs of the triangle.
c|c
Shorter Leg & Longer Leg [0.8em]
8/2= 4 & sqrt(3)* 4= 4sqrt(3)
Note that the longer leg of the right triangle is also its height. This means that the height of the triangle, and therefore the height of the trapezoid, is 4sqrt(3) feet. Furthermore, since the opposite sides of a rectangle are congruent, the major base of the trapezoid is divided into segments that measure 4 feet and b.
We will use the Segment Addition Postulate to find the value of b.
4+b= 15 ⇔ b=11feet
We now know that the length of the major base of the trapezoid is 15 feet, the length of the minor base is 11 feet, and the length of the height is 4sqrt(3) feet.
Finally, we will substitute these values into the formula for the area of the trapezoid and simplify.
