Arectangle is removed from a right triangle to create the shaded region shown below. find the area of the shaded region. be sure to include the correct unit in your answer.

29.5 yd²

Step-by-step explanation:

First we find the area of the triangle.

The base of the triangle is 5+4 = 9 yd.

The height of the triangle is 6+5 = 11 yd.

The formula for the area of a triangle is A = 1/2bh; this gives us

A = 1/2(9)(11) = 1/2(99) = 49.5 yd²

Next we find the area of the rectangle that is removed.  The length of the rectangle is 4 and the width is 5.  The area of a rectangle is given by

A = l*w; for our rectangle, we have

A = 4(5) = 20 yd²

The shaded region will have an area of

49.5 yd² - 20 yd² = 29.5 yd²

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

tap for more

m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.