In the figure ,ABC is an equilateral triangle and DEFG is trapezium • find the area of shaded equilateral triangle and trapezium
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Answer:
Area of shaded region =19.3cm ^2
Step-by-step explanation:
Given, ΔABC is an equilateral triangle the length of whose side is equal to 10 cm, and ΔDBC is right-angled at D
and BD=8cm.
From figure:
Area of shaded region = Area of ΔABC− Area of ΔDBC.
Area of ΔABC:
Area = √3 = 43.30
4
So area of ΔABC is 43.30cm ^2
Area of right ΔDBC:
Area = 2
1
×base×height.
From Pythagoras Theorem:
Hypotenuse
2
= Base
2
+ Height
2
BC
2
=DB
2
+Height
2
100−64=Height
2
36=Height
2
or Height =6
equation (2)⇒
Area =
2
1
×8×6=24
So area of ΔDBC is 24cm ^2
Area of shaded region =43.30−24=19.30
Therefore, Area of shaded region =19.3cm ^2
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