Geometry
# Area of Triangles

The rectangle in the diagram has an area equal to 640 \(\text{cm}^2\).

Points B and F are midpoints of sides AC and AE, respectively.

What is the area of triangle BDF in \(\text{cm}^2?\)

In a large equilateral triangle, we draw the incircle. We then draw a smaller equilateral triangle in the incircle.

What is the ratio of the area of the smaller equilateral triangle to that of the larger equilateral triangle?

A triangle has sides 15, 41, and 52. What is its area?

If \(AB = 10\) and \(BD = 8\), then what is the area of \( \triangle ABC\)?

The diagram above shows a triangle, it is known that \(ADEF\) is a parallelogram, \(X\) is a point on line \(AB\), \(Y\) is a point on line \(AC\). If the area of \(\triangle XEF\) is 1, then the area of \(\triangle DEY\) is...

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