The base of an isosceles trapezoid is 17 and 27 cm, and the acute angle is 60 “. Find its perimeter.

| November 22, 2020 | education

If we omit the heights from obtuse angles, then we divide the trapezoid into a rectangle and 2 identical (because the trapezoid is isosceles) right-angled triangles.
Consider a triangle.
We know one angle – 60 degrees. Hence the second angle = 30 degrees.
In a right-angled triangle opposite an angle of 30 degrees lies a side equal to 1/2 of the hypotenuse. The length of this side can be found as follows:
Since we have omitted the heights, the larger base = 27cm is divided by 17cm (side of the rectangle) and 2 identical segments:
(27-17) / 2 = 5cm
So the side opposite to the angle of 30 degrees is 5. Therefore, the hypotenuse is 5 * 2 = 10cm
Now we know all sides of the trapezoid.
Find the perimeter:
P = 27 + 17 + 10 + 10 = 64cm
Answer: P = 64cm



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