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Problem of the Week
Problem B
Shape Up

Determine the area of each of the four shapes below. In order to find the area, you may divide each shape up into other shapes in any way you need to.

Note: All linear measures are in cm. Shape 1 has a vertical line of symmetry, Shape 2 has a horizontal line of symmetry, and Shape 3 has both a horizontal and a vertical line of symmetry. All angles in Shape 3 are right angles.

Shape 1 is a four sided polygon. It has two horizontal sides with top side of length 5 and bottom side of length 7. The distance between the top and bottom sides is 4 units. Shape 2 is a composite shape made up of a square of side length 4 and a triangle. The base of the triangle runs vertically and is placed along one side of the square making a shape that looks like an arrow pointing right. The base of the triangle extends beyond the square by 2 units above and 2 units below. The height of the triangle, which runs horizontally, is 4 units.

Shape 3 is a composite shape made up of three side by side rectangles: The middle rectangle has horizontal sides of length 8 and vertical sides of length 4. The left and right rectangles are identical. The top side of the left rectangle has length 1 and is 1 unit below the top side of the middle rectangle. Shape 4 is a four sided polygon with two vertical sides of length 4 and 5 and one horizontal side of length 8.