In an isosceles trapezoid ABCD, points F and G are the midpoints of the lateral sides AB and CD, respectively

| September 16, 2021 | education

In an isosceles trapezoid ABCD, points F and G are the midpoints of the lateral sides AB and CD, respectively, the segment BN is the height of the trapezoid. Find the perimeter of the quadrilateral NFGD if the middle line of the trapezoid is 10 cm and its side is 8 cm.

Let’s draw a segment BE parallel to CD, we get an isosceles triangle ABE, and which AB = BE, BN is the height of the triangle, and FK is the middle line of the triangle.

The height BN divides the AE side into equal parts, since the ABE triangle is isosceles, therefore FN is the middle line of the ABE triangle, and is parallel to BE, and therefore parallel to the SD.

The angle BAC = BEA, as the angles at the base of an isosceles triangle, and the angle BEA = angle FNA, since BE is parallel to FN and they intersect AE, then the triangle AFN is isosceles and AF = AN = AB / 2 = 8/2 = 4 cm.

NFGD parallelogram with sides FG = ND = 10 cm, FN = GD = 4 cm.

P = 2 * (10 * 4) = 28 cm.

Answer: P = 28 cm.



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