The area of the parallelogram ABCD is 151. Find the area of the parallelogram A’B’C’D ‘
| May 3, 2021 | education
The area of the parallelogram ABCD is 151. Find the area of the parallelogram A’B’C’D ‘, the vertices of which are the midpoints of the sides of this parallelogram.
Let’s connect points A1C1 and lower the height B1H to it. The area of the parallelogram A1BCC1 is equal to half the area of the parallelogram ABCD.
Sa1vss1 = A1C1 * B1H = Saavsd / 2 = 151/2 = 75.5 cm2.
Consider a triangle A1B1C1, the area of which is equal to:
Sa1b1s1 = A1C1 * B1H / 2 = Sa1vss1 / 2 = 75.5 / 2 = 37.75 cm2.
Since A1B1C1D1 is a parallelogram, the diagonal divides it in half, then Sa1b1c1D1 = 2 * Sa1b1c1 = 37.75 * 2 = 75.5 cm2.
Answer: The area of the parallelogram A1B1C1D1 is 75.5 cm2.
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