In an equally femoral trapezoid ABCD, the height lowered from the apex B to the larger base AD is 4 cm

| July 6, 2021 | education

In an equally femoral trapezoid ABCD, the height lowered from the apex B to the larger base AD is 4 cm and divides AD into segments equal to 5 cm and 9 cm. What is the area of the trapezoid?

Since to calculate the area of a trapezoid, you need to multiply its height by half the sum of its bases:

S = h • (a + b) / 2,

then first of all, it is necessary to find their length.

Since the height of the ВН divides the larger base of the blood pressure into segments, which are equal to 5 and 9 cm, then:

AD = AH + HD;

AD = 5 + 9 = 14 cm.

The segments AH and KD are equal to each other, since the trapezoid is isosceles.

The smaller base of the BC is equal to the segment of the larger base, which is located between the heights of the ВН and СK. Based on this:

BC = НK = AD – AH – KD;

BC = НK = 14 – 5 – 5 = 4 cm.

S = (14 + 4) / 2 * 4 = 9 4 = 28 cm2.

Answer: the area of the trapezoid is 28 cm2.



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