The figure represents the overhead view of a deck surrounding a hot tub what is the area of the deck round to the nearest 10th

r = 2.7 m

R = ( 5.4 : 2 ) + 2.2 = 2.7 + 2.2 = 4.9 m

The area of the deck:

A = R² π - r² π = ( R² - r² ) π = ( 4.9² - 2.7² ) π =

= ( 24.01 - 7.29 ) π = 16.72 π = 1.72 · 3.14 ≈ 52.5 m²

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4