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3 years ago

Express the area of the entire rectangle.

Mathematics

1 answer:

Cloud [144]3 years ago

7 0

Answer:

$\huge\boxed{A=x^2+12x+35}$

Step-by-step explanation:

The formula of an area of a rectangle:

$A=lw$

l - length

w - width

We have

$l=x+7\\\\w=x+5$

Substitute:

$A=(x+7)(x+5)$

Use FOIL (a + b)(c + d) = ac + ad + bc + bd

$A=(x)(x)+(x)(5)+(7)(x)+(7)(5)\\\\A=x^2+5x+7x+35$

combine like terms

$A=x^2+(5x+7x)+35\\\\A=x^2+12x+35$

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Answer:

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2 years ago

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2 years ago

Please help me i need to find the area of shaded region please help me

Montano1993 [528]

Answer:

Part 1) $A=60\ ft^2$

Part 2) $A=80\ cm^2$

Part 3) $A=96\ m^2$

Part 4) $A=144\ cm^2$

Part 5) $A=13\ m^2$

Part 6) $A=(49\pi -33)\ in^2$

Step-by-step explanation:

Part 1) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle

The area of rectangle is equal to

$A=bh$

where

b is the base of rectangle

h is the height of rectangle

$A=(12)(7)-(8)(3)\\A=84-24\\A=60\ ft^2$

Part 2) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior square

The area of square is equal to

$A=b^2$

where

b is the length side of the square

$A=(12)(8)-(4^2)\\A=96-16\\A=80\ cm^2$

Part 3) we know that

The area of the shaded region is equal to the area of four rectangles plus the area of one square

$A=4(4)(5)+(4^2)\\A=80+16\\A=96\ m^2$

Part 4) we know that

The shaded region is equal to the area of the complete square minus the area of the interior square

$A=(15^2)-(9^2)\\A=225-81\\A=144\ cm^2$

Part 5) we know that

The area of the shaded region is equal to the area of triangle minus the area of rectangle

The area of triangle is equal to

$A=\frac{1}{2}(b)(h)$

where

b is the base of triangle

h is the height of triangle

$A=\frac{1}{2}(6)(7)-(4)(2)\\A=21-8\\A=13\ m^2$

Part 6) we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

The area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

$A=\pi (7^2)-(3)(11)\\A=(49\pi -33)\ in^2$

6 0

3 years ago