Question

In the figure ,ABC is an equilateral triangle and DEFG is trapezium • find the area of shaded equilateral triangle and trapezium​

Answer 1

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