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mojhsa [17]
3 years ago
7

Ans with steps.. Tysm Plzz asap!!

Mathematics
2 answers:
WARRIOR [948]3 years ago
5 0

Answer:

10x^2 + 8x

Step-by-step explanation:

Area of the outer rectangle = 5x(3x + 2) = 15x^2 + 10x

Area of the inner rectangle = x(5x - 2) = 5x^2 - 2x

Area of the shaded region = (15x^2 + 10x) - (5x^2 - 2x)

= 10x^2 + 8x

Marrrta [24]3 years ago
3 0

5x(3x + 2) - x(5x - 2) required expression.

Step-by-step explanation:

I get there are 2 rectangles in figure.

How can I get the area of shaded region? What if, I subtract the area of inner rectangle from outer rectangle. Ya It will surely work (⌒o⌒).

Now,

Area of outer rectangle = \sf length \times  breadth

5x \times (3x + 2)

5x(3x + 2)

Again,

Area of inner rectangle = \sf length \times  breadth

=x \times (5x - 2)

=x(5x - 2)

\sf Area \:of \:Shaded\: region = \: Area_{\:outer}-Area_{\:inner}

\sf \: 5x(3x + 2) - x(5x - 2)

If We simplify further then,

= 15x² + 10x - 5x² + 2x

= 10x² + 12x

Area of shaded region is 10x² + 12x in a simple way.

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Find the area of the shaded portion in the circle.
Anastasy [175]
See the attached picture to better understand the problem

we know that
<span>the area of the shaded portion in the circle=area 1+area 2

step 1
find area 1
area 1=area of semi circle
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diameter=12 units
radius r=12/2----> 6 units

r=6 units
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step 2
find the area 2

area 2=area sector CADC-area triangle ACD

in the right triangle ABC
BC=3
AC=r-----> AC=6
AB=?
applying Pythagoras Theorem
AC²=AB²+BC²------> AB²=6²-3²-----> AB²=27----> AB=3√3 units
area triangle ACD=b*h/2
b=2*3√3---> 6√3 units
h=3 units
area triangle ACD=6√3*3/2----> 9√3 units²-----> 15.59 units²

find the angle ACB
tan ∠ACB=AB/BC-----> 3√3/3---> √3
∠ACB=arc tan (√3)-----> 60°

the central angle ACD=60*2-----> 120°


area of sector CADC=(120/360)*pi*r²----> (120/360)*pi*6²---> 37.68 units²
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area 2=37.68-15.59----> 22.09 units²

step 3
the area of the shaded portion in the circle=area 1+area 2
the area of the shaded portion in the circle= 56.52 +22.09----> 78.61 units²

the answer is
the area of the shaded portion is 78.61 units²

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