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Aneli [31]
2 years ago
6

Find the area of the shaded region. Express your answer in terms of \piπ​ and do not round any numbers.

Mathematics
1 answer:
Feliz [49]2 years ago
6 0

Answer:

The strategy is to find out the total area and find the area of the 3 circles then subtract the sum of the circles' are from the total area

Total area = (length * width) = ( 3+6+9+12) * 18 = 540 sq. inch

3 Circles area = πr₁² + πr₂² + πr₃²

  • r₁= 12/2 = 6 in
  • r₂ = 9/2 = 4.5 in
  • r₃ = 6/2 = 3 in

πr₁² + πr₂² + πr₃²

π(6²) + π(4.5)² + π(3)²

= 36π + 20.25π + 9π

= 65.25π

Shaded area = 540 - 64.25π = 335.011 sq. in

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Area triangles? it says show work so pls do
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\large{\underline{\underline{\pmb{\sf {\color {blue}{Solution:}}}}}}

Given,

Area = 225 yd²

Base = 30 yd

Height = [To be calculated]

To find:

The height of the given triangle.

We know that, area of a triangle is:

\frac{1}{2}  \times (b \times h) \\  \\  \leadsto \frac{1}{2} \times (30 \times h) \\  \\  \leadsto \frac{1}{2}   \times 30h \\  \\  \leadsto  \frac{1}{ \cancel{2}} \times  \cancel{30}h \\  \\  \leadsto1 \times 15h \\  \\  \leadsto \: h = 15 \: yd

Therefore, the require height is 15 yd.

\green\starProof:

\frac{1}{2}  \times (b \times h) \\  \\  \leadsto \frac{1}{2}  \times (30 \times 15) \\  \\  \leadsto \frac{1}{ \cancel{2}}   \times  \cancel{450} \\  \\  \leadsto1 \times 225  \\  \\  area = 225  {yd}^{2}

\boxed{ \frak \red{brainlysamurai}}

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