In trapezoid ABCD, the bases of AD and BC are 24 and 6, respectively. Point P is the intersection point of the diagonals.

| November 17, 2020 | education

In trapezoid ABCD, the bases of AD and BC are 24 and 6, respectively. Point P is the intersection point of the diagonals. Find the ratio of the area of a trapezoid ABCD to the area of a triangle APD

In trapezoid ABCD, the bases of AD and BC are 24 and 6, respectively. Point P is the intersection point of the diagonals. Find the ratio of the area of a trapezoid ABCD to the area of a triangle APD
Two diagonals divide the trapezoid ABCD into two similar triangles: BCP and ADP. In similar triangles their heights h1 and h2 are also similar.h1 / 24 = h2 / 6. h2 = h1 / 4
h1 + h2 = h.h1 + h1 / 4 = 5 * h1 / 4. h is the height for the trapezoid.
5 * h1 / 4 = h
Trapezoid area S1 = (24 + 6) * h / 2 = 15 * h. Area triangle APD S2 = 24 * h1 / 2.
S1 = 15 * h = 15 * 5 * h1 / 4.
s1 / s2 = 15 * 5 * h1 / 4: 24 * h1 / 2 = 25/16



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