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Area of Triangles

You know that Area = base x height / 2, but what other ways are there to find the area of a triangle? Brace yourself for some potent formulae.

Level 1


The rectangle on the figure has an area equal to 640 \(\text{cm}^2\). The points B and F are midpoints of the sides AC and AE, respectively. What is the area of the triangle BDF in \(\text{cm}^2\)?

In a large equilateral triangle, we draw the incircle. In the incircle, we draw another equilateral triangle.

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

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

\( \triangle ABC\) is a right triangle and line segment \(AD\) is an altitude.
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...

This is one part of 1+1 is not = to 3.


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