AMC8 2004

AMC8 2004 · Q14

AMC8 2004 · Q14. It mainly tests Area & perimeter, Coordinate geometry.

What is the area enclosed by the geoboard quadrilateral below?

下面几何板上的四边形围成的面积是多少？

(A) 15 15

(B) 18 1/2 18 1/2

(D) 27 27

(E) 41 41

Answer

Correct choice: (C)

正确答案：（C）

Solution

Square: $10 \times 10 = 100$ Region $A$: $3 \times 5 = 15$ Region $B$: $\frac{1}{2} \times 6 \times 7 = 21$ Region $C$: $\frac{1}{2} \times 1 \times 3 = 1\frac{1}{2}$ Region $D$: $\frac{1}{2} \times 4 \times 5 = 10$ Region $E$: $\frac{1}{2} \times 6 \times 10 = 30$ The area is $100 - (15 + 21 + 1\frac{1}{2} + 10 + 30) = 100 - 77\frac{1}{2} = 22\frac{1}{2}$ square units.

正方形：$10 \times 10 = 100$ 区域 $A$：$3 \times 5 = 15$ 区域 $B$：$\frac{1}{2} \times 6 \times 7 = 21$ 区域 $C$：$\frac{1}{2} \times 1 \times 3 = 1\frac{1}{2}$ 区域 $D$：$\frac{1}{2} \times 4 \times 5 = 10$ 区域 $E$：$\frac{1}{2} \times 6 \times 10 = 30$ 面积为：$100 - (15 + 21 + 1\frac{1}{2} + 10 + 30) = 100 - 77\frac{1}{2} = 22\frac{1}{2}$ 平方单位。

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