Find the area of the following shape. you must show all work to receive credit. (10 points)

figure abcdef is shown. a is located at 5, negative 8. b is located at 11, negative 8. c is located at 11, 0. d is located at 6

answer:

the area of the shape is 51.5

step-by-step explanation:

*at first we will find the area of the rectangle whose vertices are:

(0 , 0) , (11 , 0) , (11 , -8) , (0 , -8)

its length = 11 - 0 = 11 and its width = 0 - (-8) = 8

its are = 11 × 8 = 88⇒(1)

*now we will subtract area of three figures from the area of the rectangle to get the area of the figure abcdef

*the first figure is the trapezium whose vertices are:

c (11 , 0) , d (6 , -3) , e (4 , -3) , (4 , 0)

the length of the two parallel bases are :

b1 = 6 - 4 = 2 , b2 = 11 - 4 = 7

the length of its height = 0 - (-3) = 3

its area = ⇒(2)

*the second figure is the trapezium whose vertices are:

(0 , 0) , (4 , 0) , e (4 , -3) , f (0 , -6)

the length of the two parallel bases are :

b1 = 0 - (-3) = 3 , b2 = 0 - (-6) = 6

the length of its height = 4 - 0 = 4

its area = ⇒(3)

*the third figure is the triangle whose vertices are;

f (0 , -6) , (0 , -8) , a (5 , -8)

the length of its base = 5 - 0 = 5

the length of its height = (-6) - (-8) = 2

its area = ⇒(4)

then the area of abcdef = (1) - (2) - (3) - (4) = 88 - 13.5 - 18 - 5 = 51.5

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step-by-step explanation: