A parallelogram features sides measuring 60 m and 40 m alongside an 80 m diagonal; its area is:__________?
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Answer: C. 600√15 sq.m
Explanation
A parallelogram features sides measuring sixty and forty meters alongside an eighty-meter diagonal. The diagonal divides the parallelogram into two identical triangles with side lengths sixty, forty, and eighty. Applying Heron formula to one triangle and doubling the area gives six hundred root fifteen square meters. Parallelograms are composed of two congruent triangles sharing a common diagonal side. Heron formula calculates triangle area using semi-perimeter and side lengths without needing altitude angles. Calculating the area of one triangle and multiplying by two yields the total parallelogram surface area.
Surveyors and civil engineers use triangle area formulas to calculate irregular land parcel dimensions. Structural analysis requires determining surface areas of quadrilateral panels and bracing elements. Advanced geometry problems test proficiency in Heron formula and multi-part shape calculations. Option A represents an incorrect arithmetic calculation that ignores the square root radical terms. Option B suggests a severely understated area not supported by the side length dimensions. Option D proposes an incorrect radical coefficient for the calculated triangle surface area.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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