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puteri [66]
3 years ago
9

A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sur

e to include the correct unit in your answer.

Mathematics
2 answers:
Mashcka [7]3 years ago
7 0
The sides of a right triangle are
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
hoa [83]3 years ago
4 0

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

A_R=l\times b

A_R=8\times 6=48

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

l_1=8-5=3

l_2=6-4=2

The area of right angled triangle is

A_T=\frac{1}{2}\times l_1\times l_2

A_T=\frac{1}{2}\times 3\times 2=3

The area of triangle is 3 square units.

The area of shaded region is

A=A_R-A_L=48-3=45

Therefore the area of shaded region is 45 square units.

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Liz wants to buy a shirt for $25 how much will liz s shirt cost in Springfield rounded up to the nearest cent
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Multiply the polynomials.<br> (4x- + 4x + 6)(7x + 5)
SashulF [63]

\implies {\blue {\boxed {\boxed {\purple {\sf {   \: 28 {x}^{3}  + 48 {x}^{2}  + 62x + 30}}}}}}

\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}

(4 {x}^{2}  +  4x + 6)(7x + 5)

= \: 7x(4 {x}^{2}  + 4x + 6) + 5(4 {x}^{2}  + 4x + 6)

=  \: 28 {x}^{3}  + 28 {x}^{2}  + 42x + 20 {x}^{2}  + 20x + 30

Combining like terms, we have

=  \: 28 {x}^{3}  + (28 {x}^{2}  + 20 {x}^{2} ) + (42x + 20x) + 30

=  \: 28 {x}^{3}  + 48 {x}^{2}  + 62x + 30

\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}

3 0
3 years ago
HLEPP PLEASEEEEEEEE hsnsnansh
miss Akunina [59]
M = -1/2
B = 1

Equation shown is y = mx + b
4 0
3 years ago
What is the surface area of the triangular prism shown?
Lunna [17]

Answer:

The first step that we are going to do is to solve the area of the top rectangle.  We are given a width of 15 cm and a length of 25 cm so we can just multiply them against each other to get the area.

Area = l * w

Area = 25\ cm * 15\ cm

Area = 375\ cm^2

The second side that we are going to solve for is the bottom rectangle.  We are given a width of 12 cm and a length of 25 cm so lets just multiply them against each other to get the area.

Area = l * w

Area = 25\ cm * 12\ cm

Area = 300\ cm^2

The next area that we are going to determine is the back rectangle which has a width of 9 cm and a length of 25 cm so lets just multiply them against each other to get the area.

Area = l * w

Area = 25\ cm * 9\ cm

Area = 225\ cm^2

The final area that we have to determine are the side triangles.  After determining the area of one triangle we will have to multiply it by 2 to get the area for both of the triangles.  We are given a base of 12 cm and a height of 9 cm so lets just use the formula to find the area.

Area = \frac{1}{2}* b*h

Area = \frac{1}{2}* 12\ cm*9\ cm

Area = 54\ cm^2

Multiply it by two to get the area for both of the triangles.

Area = 54\ cm^2 * 2

Area = 108\ cm^2

Finally, we are onto the last part which is to add up all of the areas and get the surface area after we combine everything.

Area_{total}=375\ cm^2 + 300\ cm^2 + 225\ cm^2 + 108\ cm^2

Area_{total}=1008\ cm^2

Therefore, our final answer is option B, 1008 cm^2

Hope this helps!

4 0
2 years ago
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