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Geometry

#### Challenge Quizzes

If the sides of a square are increased by 1%, then by what percent will the area of this square be increased?

The above figure shows five congruent rectangles. A trapezoid is drawn in such a way that its vertices coincide with vertices of some of the rectangles. What percentage of the figure is shaded?

In the diagram to the right, quadrilateral $$ABCD$$ is a parallelogram and $$M$$ is the midpoint of $$\overline{DC}.$$

If the area of $$\triangle BNC$$ is $$42,$$ what is the area of $$\triangle MNC?$$

In rectangle ABCD (below left), $$AB=3$$ and $$BC=5$$. The corner at C is folded up (below right) and lands on $$\overline{AB}$$ so that $$AC=2$$ and $$CB=1$$.

The area of quadrilateral CPNM can be written as $$\frac{m}{n}$$, where m and n are positive, coprime integers. Find $$m+n$$.

What is the area of a rhombus of side 13 such that the sum of its two diagonals is 34?

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