Coat of arms

The class created its own coat of arms, which had a shape composed of an isosceles trapezoid ABCD (shorter base is a = 4.5 cm long, longer 2a = 9 cm, trapezoid height 6 cm) and a semicircle with center S and diameter AB. The trapezoid was formed by three identical isosceles triangles. Pupils painted half of the semicircle and the middle field of the trapezoid (middle triangle) gray. How many cm ^ 2 areas of the coat of arms was gray? Round the result to one decimal place.

Correct answer:

S =  29.4043 cm2

Step-by-step explanation:

a=4.5 cm c=2 a=2 4.5=9 cm v=6 cm  r=a=4.5=29=4.5 cm  S1=2a+c v=24.5+9 6=281=40.5 cm2 S2=π r2/2=3.1416 4.52/231.8086 cm2  S=S1/3+S2/2=40.5/3+31.8086/2=29.4043 cm2

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