Assessment
This assessment consists of four designs made on a geoboard. The students must determine the area of
each. The four designs are divided between two pages; the teacher may assign all four designs or two
or allow the student to choose.
All designs can be divided into parallelograms, triangles, and trapezoids. The sum of the areas of the
composite polygons gives the area of the design.
The visual nature of the assessment allows students to find the solutions in multiple ways, the most
common ones are shown below. Students may intuitively solve the areas but should be encouraged to
justify their solutions with explanations and with formulas.
A
The design splits into congruent trapezoids resulting in the
following equation:
2(
b1 + b2
4+1
• h) = 2(
2
2
• 2) = 10
A
A1
(see A1)
Or the two trapezoids can be rotated into a long parallelogram
with a base of five and a height of two, giving an area of 10. (see A1)
b • h = A 5 • 2 = 10
A
The design can be divided into two congruent rectangles, two isosceles
triangles, and two scalene triangles. The rectangles have a combined
area of four, the isosceles triangles can be rotated to form a square with
an area of four. The scalene triangles can be rotated to form a rectangle
with an area of two. The total for all six polygons is 10. (see A2)
B
The design can be cut into four congruent trapezoids. With
bases of two and one and a height of two, each has an area
of three. Three times four is 12. (see B1)
4(
b1 + b2
2+1
• h) = 4(
2
2
A2
B
B1
• 2) = 12
Two of the trapezoids can be rotated to form a rectangle with dimensions
of two by three and an area of six. Two pairs make an area of 12.
The design can also be divided into four congruent rectangles and
four congruent triangles. The rectangles each have an area of two for
a combined area of eight. The triangles have a base of one and height
of two resulting in an area of one and a combined total of four. The
combined areas of rectangles and triangles is 12. (see B2)
AREA FORMULAS
65
B
B2
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