SOLUTION: ABCD is a square of side 4 cm. Equilateral triangles are constructed on the sides of the square. Find the length of EH and the area of triangle EDH. <img src="https://i.ibb.

Question 1205070: ABCD is a square of side 4 cm. Equilateral triangles are constructed on the sides of the square.
Find the length of EH and the area of triangle EDH.

Found 2 solutions by math_tutor2020, Edwin McCravy:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Any square has all four interior angles of 90 degrees each.
Angle ADC = 90

Any equilateral triangle has each interior angle of 60 degrees.
Angle EDA = angle CDH = 60

Focus on the angles around point D.
They must add to 360 to do a full sweep or full rotation.
(angleEDH) + (angleEDA) + (angleADC) + (angleCDH) = 360
(x) + (60) + (90) + (60) = 360
x + 210 = 360
x = 360-210
x = 150

Angle EDH = 150 degrees
Sides ED and DH of triangle EDH are 4 cm each.

For triangle EDH we have the SAS (side angle side) case here, which means we can use the law of cosines to find the missing side.

d^2 = e^2 + h^2 - 2*e*h*cos(D)
(EH)^2 = (DH)^2 + (ED)^2 - 2*DH*ED*cos(angle EDH)
(EH)^2 = 4^2 + 4^2 - 2*4*4*cos(150)
(EH)^2 = 59.712813
EH = sqrt(59.712813)
EH = 7.727407

Segment EH is roughly 7.727 cm long. Round this value however needed or however your teacher instructs.

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

The student also asked for the area of triangle EDH. math_tutor2020 has found that
Angle EDH = 150 degrees
Sides ED and DH of triangle EDH are 4 cm each.
For triangle EDH we have the SAS (side angle side)...
Anytime we have the SAS case and want the area of the triangle, we should use the formula for the area: Edwin

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