In trapezoid ABCD: the bases of BC and AD are equal to 2 cm and 8 cm, and the diagonal AC = 4 cm
| July 19, 2021 | education
In trapezoid ABCD: the bases of BC and AD are equal to 2 cm and 8 cm, and the diagonal AC = 4 cm In what relation does the AC diagonal divide the area of the trapezoid?
The height of the trapezoid h will be the height of triangles ABC and ACD at the same time. The base of the first triangle is BC, the second is AD.
Areas of triangles:
SABC = (BC * h) / 2;
SACD = (AD * h) / 2;
Area Ratio:
SABC / SACD = ((BC * h) / 2) / ((AD * h) / 2) = BC / AD = 2 cm / 8 cm = 1/4.
Answer: The diagonal of a trapezoid divides its area into two parts in a ratio of 1/4.
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