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Figure out the Area (Challenging)
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Science
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Can you name the areas to the various shapes?
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Get out your paper and pencil (and probably calculator); it's time for some challenging area problems! *Note: The ratio of RB to BH is 4 to 1. **Note: Round #10 to a whole number!!!
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Number (Shape)
Area
Explanation
1. (Square)
16*16=256
2. (Triangle)
Pythagorean Triple: (7, 24, 25), so (24*7)/2 = 84
3. (Circle)
(pi)(radius)^2
4. (Square)
Line cuts square into 2 45-45-90 triangles with sides x, x, x*root(2). So the side=11, 11*11=121
5. (Regular Pentagon)
5*(16/2)*11 = 440
6. (Equilateral Triangle)
Area = (side^2)*(root(3))/4. So simplify to 12/4=3
7. (Trapezoid)
A=height*(base1+base2)/2. Cut trapezoid into two triangles and a rectangle. Figure out sides of triangles.
8. (Rhombus)*
Use the ratio to figure out the length of RB and therefore RH (10). Then 10*6=60.
9. (Kite)
Split kite into 4 triangles. Use 45-45-90 triangles on top, and figure out bottom triangles from there. Then you'll get the bisectors.
10. (Regular Octagon)**
Area of Square - Area of Outer Triangles = Area of Octagon.
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