The area of the parallelogram ABCD is 184. Point E is the midpoint of side AB. Find the area of the trapezoid EBCD.
| February 11, 2021 | education
1. A, B, C, D – the tops of the parallelogram. S – area. h = height.
2. S trapezium EВСD = (DE + BC) / 2 x h.
BC = AD, since the sides of the parallelogram that are opposite each other (opposite), are equal.
DE = 1 / 2AD according to the problem statement.
3. Substitute 1/2 AD instead of DE and AD instead of BC into the original expression:
S trapezium EВСD = (AD / 2 + AD) 2 x h = 3AD / 4 x h.
AD x h is the S parallelogram. SD x h = 184.
S trapezium EВСD = 184 х 3/4 = 138 units of measurement².
Answer: S trapezium EВСD = 138 units of measurement².
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