Subjects geometry

Triangle Area 5A1D54

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1. **State the problem:** Calculate the area of the triangles outlined by dotted lines. 2. **Formula for the area of a triangle:** The area $A$ of a triangle is given by $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify base and height:** To find the area, we need the length of the base and the corresponding height (perpendicular distance from the base to the opposite vertex). 4. **Calculate the area:** Multiply the base length by the height, then divide by 2. 5. **If coordinates are given:** Use the coordinate geometry formula for area: $$A = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$$ 6. **Explain simplification:** This formula calculates the absolute value of the determinant formed by the vertices' coordinates, giving the area directly. Since no specific measurements or coordinates are provided, please provide the base and height or the coordinates of the triangle vertices to calculate the exact area.