The base AD of the trapezoid ABCD is 6 cm, and its height is 4 cm. Find the area of the trapezoid if the area
| March 23, 2021 | education
The base AD of the trapezoid ABCD is 6 cm, and its height is 4 cm. Find the area of the trapezoid if the area of the triangle ABC is 6 cm2.
The first way.
The area of the trapezoid is equal to the sum of the areas of the triangles ABC and ACD.
Sasd = AD * ВН / 2 = 6 * 4/2 = 12 cm2.
Then Savs = Savs + Sasd = 6 + 12 = 18 cm2.
Second method.
The height VN of the trapezoid ABCD and the height AK of the triangle ABC have the same length.
Then the area of the triangle ABC is equal to: Savs = BC * AK / 2 = BC * VN / 2.
ВС = 2 * Saс / ВН = 2 * 6/4 = 12/4 = 3 cm.
Determine the area of the trapezium ABCD.
Savsd = (ВС + АD) * ВН / 2 = (3 + 6) * 4/2 = 36/2 = 18 cm2.
Answer: The area of the trapezoid is 18 cm2.
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