Calculate the area of triangle ABC with atthde CD , given \( \mathrm{A}(6,0), \mathrm{B}(1,5), \mathrm{C}(2,0) \), and \( \mathrm{D}(4,2) \). 5 square unlts 8 square units 10 square units 13 square unts

To calculate the area of triangle ABC with the given points A(6,0), B(1,5), C(2,0), and D(4,2), we can use the formula for the area of a triangle given the coordinates of its vertices. The formula for the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is: \[ \text{Area} = \frac{1}{2} |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| \] Given points A(6,0), B(1,5), C(2,0), and D(4,2), we can substitute these values into the formula to find the area of triangle ABC. Let's calculate the area of triangle ABC using the given points. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}\left|6\left(5-0\right)+1\times \left(0-0\right)+2\left(0-5\right)\right|\) - step1: Subtract the terms: \(\frac{1}{2}\left|6\left(5-0\right)+1\times 0+2\left(0-5\right)\right|\) - step2: Multiply the numbers: \(\frac{1}{2}\left|6\left(5-0\right)+0+2\left(0-5\right)\right|\) - step3: Remove 0: \(\frac{1}{2}\left|6\times 5+0+2\left(0-5\right)\right|\) - step4: Remove 0: \(\frac{1}{2}\left|6\times 5+0+2\left(-5\right)\right|\) - step5: Multiply the numbers: \(\frac{1}{2}\left|30+0+2\left(-5\right)\right|\) - step6: Multiply the numbers: \(\frac{1}{2}\left|30+0-10\right|\) - step7: Remove 0: \(\frac{1}{2}\left|30-10\right|\) - step8: Subtract the numbers: \(\frac{1}{2}\left|20\right|\) - step9: Calculate the absolute value: \(\frac{1}{2}\times 20\) - step10: Reduce the numbers: \(1\times 10\) - step11: Simplify: \(10\) The area of triangle ABC is 10 square units.