A field in the shape of a quadrilateral has one diagonal of $50$ m. The perpendiculars from the other two…

A field in the shape of a quadrilateral has one diagonal of $50$ m. The perpendiculars from the other two vertices to this diagonal are $24$ m and $16$ m. Find the area of the field.
  1. $1000 \text{ m}^{2}$
  2. $2000 \text{ m}^{2}$
  3. $500 \text{ m}^{2}$
  4. $800 \text{ m}^{2}$

Solution

Area $= \dfrac{1}{2}\times 50 \times (24+16) = 25 \times 40 = 1000 \text{ m}^{2}$.

Asked in: IMO

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