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Broad Topics > 2D Geometry, Shape and Space > Parallelograms

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Areas of Parallelograms

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the area of a parallelogram defined by two vectors?

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Floating in Space

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.

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Similarly So

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

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Linkage

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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Arrowhead

Stage: 4 Challenge Level: Challenge Level:1

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

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Quad in Quad

Stage: 4 Challenge Level: Challenge Level:1

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

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Roaming Rhombus

Stage: 4 Challenge Level: Challenge Level:1

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .

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Cut and Make

Stage: 2 Challenge Level: Challenge Level:1

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?