Find the area of trapezoid DUCK shown below.

area of a trapezoid = (1/2)(first base + second base)(height)

 

5² + height² = 13² → height = \(\sqrt{144}=12\)

 

first base = \(5+15+\sqrt{20^2-12^2}=5+15+\sqrt{256}=36\)

 

second base = 15

 

area = (1/2)(36 + 15)(12) = (6)(51) = 306 sq. un.

area of trapezoid = height * (a + b) / 2

 

Height = sqrt(13² - 5²) = sqrt(144)     »»»     sqrt(144) = 12

 

a = 15

 

b = DK = 5 + 15 + sqrt(20² - height²)     »»»    20 + sqrt(20² - 12²) = 20 + sqrt(256) = 36

 

area = 12 * (15 + 36) / 2     »»»     6 * 51 = 306 units²