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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 above diagram, 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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