In an isosceles trapezoid ABCD, the diagonal is perpendicular to the side of the trapezoid. Find the area of the trapezoid

| December 3, 2020 | education

In an isosceles trapezoid ABCD, the diagonal is perpendicular to the side of the trapezoid. Find the area of the trapezoid if the large base is 12 cm and one of the corners of the trapezoid is 120 degrees.

The sum of the angles adjacent to the side of the trapezoid is 180 °.
The angles at the bases of an isosceles trapezoid are equal.
∟ABC = ∟DCB = 120 °,
∟BAC = ∟CDA = 60 °.
In a right-angled triangle ABD ∟ADB = 90 ° – 60 ° = 30 °,
AB = AD / 2 = 6 cm (leg opposite an angle of 30 °).
CD = AB = 6cm
∟CDB = ∟CDA – ∟ADB = 60 ° – 30 ° = 30 °
∟CBD = ∟ADB = 30 ° (criss-cross)
Then triangle BCD is isosceles
BC = CD = 6 cm
Let’s draw the height of the VN.
From the right-angled triangle ABN:
VN = AB sin60 ° = 6 √3 / 2 = 3√3 cm
Area abcd = (AD + BC) / 2 BH = (12 + 6) / 2 3√3 = 9 3√3 = 27√3 cm ^ 2



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