# In the trapezoid ABCD AD = 4, BC = 1, and its area is 35. Find the area of triangle ABC

May 31, 2020 | Education

| The area of the trapezoid is h * (a + b) / 2, where a and b are the bases of the trapezoid, h is the height of the trapezoid.

h trapezoid * (4 + 1) / 2 = 35 (according to the condition of the problem)

h = 35 / 2.5 = 14

Draw the height of the triangle ABC, as shown in the figure.

h of a triangle = h of a trapezoid, since they are both perpendicular to the same parallel bases of the trapezoid and form a rectangle.

S triangle = h triangle * BC / 2 = 14 * 1/2 = 7

Answer: S triangle = 7

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