Use the image to answer the question.
An illustration shows a trapezoid with top side as 4 centimeters, and the left as the longest side of 9 centimeters. The opposite parallel side on the right is 6 centimeters. A diagonal bottom side is 5 centimeters. The top side is perpendicular to the left and right sides as denoted by right two angle symbols. A perpendicular dotted line from the bottom right vertex to the left side is drawn. The dotted line makes one right angle symbol with right side and two right angle symbols with the left side. It forms a right triangle at the bottom of the trapezoid, with the 5 centimeter side as the hypotenuse.
Find the area of the quadrilateral.
To find the area of the trapezoid, we can split it into two shapes: a triangle and a rectangle.
First, we find the area of the triangle formed by the two shorter sides of the trapezoid and the diagonal bottom side. This triangle is a right triangle with sides 4 cm, 3 cm, and 5 cm.
Using the Pythagorean theorem, we can find the height of the trapezoid: h = √(5^2 - 3^2) = √(25 - 9) = √16 = 4 cm.
Therefore, the area of the triangle is (1/2) * 3 * 4 = 6 square centimeters.
Next, we find the area of the rectangle part of the trapezoid. The base of the rectangle is 6 cm, and the height is 4 cm.
Therefore, the area of the rectangle is 6 * 4 = 24 square centimeters.
Adding the area of the triangle and the rectangle together, we get the total area of the trapezoid: 6 + 24 = 30 square centimeters.
Therefore, the area of the quadrilateral is 30 square centimeters.