Volume 8 Math Stars Worksheet Page 19
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35Vol. 8 No. 5
7. [a) 14; b) 204] Students should begin their search with a system or plan. They can start by counting
the 1x1's, 2x2's, etc., and look for a pattern. The count will proceed to find one square in a 1x1, five in
a 2x2, fourteen in a 3x3, etc., or 1, 1+ 4, 1+ 4 + 9, 1+ 4 + 9 + 16, 1+ 4 + 9 + 16 + 25 + . . ..
√
8. [15
2 or 21.2 cm] The square will give the shortest diagonal. With perimeter 60 cm, the side will
+
have length 15 cm; the Pythagorean Theorem provides the diagonal length as 15
.
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2
15
9. [60%] The area of one unshaded triangle is .5 x 50 x 30 or 750 square centimeters, while the other
triangle has area .5 x 50 x 10 or 250 square centimeters. The square has total area 50 x 50 or 2500
square centimeters. Computing: total area - unshaded area = shaded area or 2500 - 1000 = 1500 or the
shaded area is 1500 square centimeters. The percent shaded is therefore 1500 ÷ 2500 or 60%.
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10. [158,184,000 plates] South Carolina Plates = 26 x 26 x 26 x 10 x 10 x 10 or 26
x 10
= 17,576,000;
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4
while North Carolina Plates = 26 x 26 x 26 x 10 x 10x 10 x 10 or 26
x 10
= 175,760,000. The
difference is 158,184,000.
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