To find the area of an acute triangle using a circumscribed rectangle, Amaurty can follow these steps:
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Determine the Vertices: Identify the coordinates of the triangle's vertices on the coordinate grid.
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Draw a Circumscribing Rectangle: Draw a rectangle that completely encompasses the triangle. The rectangle's sides will align with the axes of the coordinate grid, with its corners being the extreme points of the triangle.
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Calculate the Area of the Rectangle: Measure the length and width of the rectangle. The area can be found using the formula: \[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} \]
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Identify the Area of Right Triangles: Form right triangles by drawing lines from the triangle's vertices to the rectangle's edges. The area of these right triangles can be calculated using the formula: \[ \text{Area}_{\text{right triangle}} = \frac{1}{2} \times \text{base} \times \text{height} \]
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Subtract the Areas of the Right Triangles from the Rectangle: If there are multiple right triangles formed outside of the triangle, calculate their total area and subtract it from the area of the rectangle to find the area of the triangle: \[ \text{Area}{\triangle} = \text{Area}{\text{rectangle}} - \text{Area}_{\text{right triangles}} \]
Finding the Area in Square Units
Without the coordinates or further details of the triangle's dimensions, I can't provide a specific numeric value for the area. If you can supply the vertices of the acute triangle or the dimensions of the rectangle, I can help you calculate the exact area. Alternatively, if you have specific values from your image or problem context, feel free to share them!
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