Subjects geometry

Triangle Area 2E41C6

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1. We need to calculate the area of the blue triangle shown on the grid. 2. The vertices of the triangle are approximately at points A(2,2), B(2,6), and C(6,6). 3. The formula for the area of a triangle given coordinates is: $$\text{Area} = \frac{1}{2} \times |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$ 4. Substitute the points A(2,2), B(2,6), and C(6,6): $$\text{Area} = \frac{1}{2} \times |2(6 - 6) + 2(6 - 2) + 6(2 - 6)|$$ 5. Simplify inside the absolute value: $$= \frac{1}{2} \times |2(0) + 2(4) + 6(-4)| = \frac{1}{2} \times |0 + 8 - 24| = \frac{1}{2} \times |-16|$$ 6. Calculate the absolute value and multiply: $$= \frac{1}{2} \times 16 = 8$$ 7. Therefore, the area of the blue triangle is 8.
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