Geometry

Quadrilaterals

Quadrilaterals: Level 3 Challenges

         

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 ABCDABCD is a parallelogram and MM is the midpoint of DC.\overline{DC}.

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

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

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