The diagonal of an isosceles trapezoid divides its midline into two segments 14 and 6.

| August 15, 2021 | education

The diagonal of an isosceles trapezoid divides its midline into two segments 14 and 6. The length of the side is 10 cm. Find the area of the trapezoid.

Consider triangle ACD. So MK is the middle line of the trapezoid, then the segment OK is the middle line of the triangle ACD, then the base of AD is equal to the two middle lines of OK. AD = 2 * OK = 2 * 14 = 28 cm.

Similarly, in the triangle ABC, MO its middle line, then BC = 2 * MO = 6 * 2 = 12 cm.

Let us draw, from the vertex C, the height CH, which cuts off the segment HD from the base AD, the length of which is equal to the half-difference of the bases of the trapezoid.

НD = (АD – ВС) / 2 = (28 – 12) / 2 = 16/2 = 8 cm.

From the right-angled triangle CHD, we define the leg CH.

CH ^ 2 = CD ^ 2 – HD ^ 2 = 10 ^ 2 – 8 ^ 2 = 100 – 64 = 36.

CH = 6 cm.

Determine the area of ​​the trapezoid.

S = (AD + BC) * CH / 2 = (28 + 12) * 6/2 = 120 cm2.

Answer: The area of ​​the trapezoid is 120 cm2.



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