Trapezoid QRST has two right angles. A 5-in. altitude can be drawn dividing QRDT into a rectangle and an isosceles right triangle. The longer side of the rectangle measures 9 in. What is the area of the trapezoid?

The area of the trapezoid is 57.5 square inches

Step-by-step explanation:

we know that

The trapezoid QRST can be divided into a rectangle QRDT and an isosceles right triangle RSD

see the attached figure to better understand the problem

step 1

The area of rectangle is given by the formula

we have

----> altitude

substitute

step 2

Find the area of the isosceles right triangle

The area of triangle is given by the formula

we have

---> because is an isosceles triangle

substitute

step 3

Adds the areas

d

step-by-step explanation:

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: