What is ∆DEF area?
Geometry
Level
pending
What is the area of the triangle ?
Give your answer to 3 decimal places.
The answer is 27.713.
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1 solution
∵AE= EB= BF= FC= CD= DA.
∴AB =BC =CA= 16CM.
∴∆ABC is a Equilateral triangle.
∴(CAB)= (ABC)= (BAC)= 60°.
∵AE= EB, BF= FC.
∴EF= ½*AC= 8CM, EF//AC
∵BF= FC, AD= AC.
∴DF= ½*AB= 8CM, DF//AB
∵AD= DC, AE= EB.
∴ED= ½*CB= 8CM, ED//CB
∵ED//FB, EB//DF,
∵ED= FB, EB= DF= 8CM.
∴EDFB is a rhombus.
∴(EDF)= (EBF)= 60°.
∴∆DEF area= ½(8 * 8 * sin(60))≈ 27.713CM².