Coat of arms

The class created its 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. Three identical isosceles triangles formed the trapezoid. Pupils painted the semicircle's gray half and the trapezoid's middle field (central triangle). How many cm2 areas of the coat of arms were gray? Please round the result to one decimal place.

Correct answer:

S =  29.4 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=29.4 cm2



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