What is the area of an isosceles trapezoid with base lengths of 8 cm and 10 cm if the center

| April 28, 2021 | education

What is the area of an isosceles trapezoid with base lengths of 8 cm and 10 cm if the center of the circumscribed circle lies on a larger base?

Let’s draw the radii of the circle OB and OC, then the OBC triangle is isosceles. Let’s draw from point O the height OH to the smaller base, which will also be the median of the triangle, then BH = CH = BC / 2 = 8/2 = 4 cm.

The radii OB and OS are equal to half the length of the base AD, since point O is the center of the circle. ОВ = OC = АD / 2 = 10/2 = 5 cm.

In a right-angled triangle ОВН, according to the Pythagorean theorem, we define the length of the height ОН.

OH ^ 2 = OB ^ 2 – BH ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9.

OH = 3 cm.

Determine the area of the trapezoid.

Savsd = (AD + BC) * OH / 2 = (10 + 8) * 3/2 = 27 cm2.

Answer: The area of the trapezoid is 27 cm2.



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