Find the area of the SHADED figure

The first one is a)
And the second one is b)

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Thank you

a) 131.5 m²

b) 213.12 m²

Step-by-step explanation:

a) rectangle - circle

Radius = (14 - 2 - 2)/2 = 5

(15 × 14) - (3.14 × 5²)

131.5 m²

b) parallelogram- rectangle- trapezium + semicircle

Length of the rectangle: 20 - 6 - 3 = 11

Radius = 8/2 = 4

(15 × 20) - (4 × 11) - ½(11 + 6)(8) + ½(3.14 × 4²)

213.12 m²

a)

First one is a rectangle with two semicircles removed, which we can think of as one whole circle.  

The rectangle dimensions are 14m by 15m

The circle has a diameter of 14m - 2m - 2m = 10m.  So it has radius 5m.

Of course the area of a rectangle is length times width and the area of a cricle is πr²

So the area we seek is

A = 14×15 - π(5²) = 210 - 25π

210-25π sq meters

You didn't ask for an approximation so we'll leave it exact.  You'll have to work the calculator if they want an approximation.

b)

Ugh.  That's a parallelogram less a rectangle and a right trapezoid, with a semicircle put back in.

Parallelogram base 20 m, height 15 m.  I'm going to leave out the units for now.  Area is 20×15.

Rectangle (at bottom) 4 by (20 - 6 - 3) is 4 by 11.  Area is 4×11.

Trapezoid height 8, bases 11 and 6.  Area is 8(11 + 6)/2

Semicircle, diameter 8, radius 4.  Area is π4²/2.

A = 20×15 - 4×11 - 8(11 + 6)/2 + π4²/2

A = 188 + 8π square meters

188+8π sq meters

Again I leave any calculator work to you.

answer: 48

just remember to use pemdas:

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