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A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.

A right triangle is removed from a rectangle to create the shaded region shown below Find the area of the shaded region Be sure to include the correct unit in y class=

Respuesta :

The sides of a right triangle are
[tex]a=8-5=3 \\ b=6-4=2 \\ \\A=A_{rectangle}-A_{triangle}=8\times 6- \frac{ab}{2} =48-\frac{3\times2}{2}=48-3=45[/tex]

Answer:

The area of shaded region is 45 square units.

Step-by-step explanation:

The length of the rectangle is 8 and the breadth is 6.

Area of rectangle is

[tex]A_R=l\times b[/tex]

[tex]A_R=8\times 6=48[/tex]

The area of rectangle is 48 square units.

Since the opposite sides of a rectangle are equal, therefore the legs of the right angled triangle are

[tex]l_1=8-5=3[/tex]

[tex]l_2=6-4=2[/tex]

The area of right angled triangle is

[tex]A_T=\frac{1}{2}\times l_1\times l_2[/tex]

[tex]A_T=\frac{1}{2}\times 3\times 2=3[/tex]

The area of triangle is 3 square units.

The area of shaded region is

[tex]A=A_R-A_L=48-3=45[/tex]

Therefore the area of shaded region is 45 square units.

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