One of the diagonals of a right-angled trapezoid divides this trapezium into two right-angled isosceles triangles

univerkov | March 3, 2021 | education

One of the diagonals of a right-angled trapezoid divides this trapezium into two right-angled isosceles triangles. What is the area of this trapezoid if its smaller side is 4?

Since, by condition, triangles ABC and ACD are rectangular and isosceles, AB = BC = 4 cm, AC = CD.

The quadrilateral ABCН is a square, then AH = CH = AB = BC = 4 cm.

Let’s construct the height of CH, which is also the bisector and median in an equilateral triangle.

Then DH = AH = 4 cm, AD = AH + DH = 4 + 4 = 8 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (4 + 8) * 4/2 = 24 cm2.

Answer: The area of the trapezoid is 24 cm2.

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