Geometry

Area of Triangles

Area of Triangles - Shoelace Formula

         

Let A=(5,2)A=(5,2) and B=(6,5)B=(6,-5) be two vertices of triangle ABC.ABC. If the area of the triangle is 9,9, which of the following are possible coordinates for the third vertex?

Consider a square ABCDABCD with side length 19.19. If we let MM and NN be the midpoints of BC\overline{BC} and CD,\overline{CD}, respectively. What is the area of AMN?\triangle AMN?

Statement 11: If the area of the triangle bounded by the lines y=x,x+y=8y=x, x+y=8 and the line through P=(h,k)P=(h,k) parallel to the xx-axis is 4h2,4h^2, then PP lies on either of the two lines represented by 4x2+8yy216=0.4x^2+8y-y^2-16=0.

Statement 22: The area of the triangle bounded by the lines y=x,x+y=8y=x, x+y=8 and the xx-axis is equal to half of the area of the triangle bounded by the line x+y=8x+y=8 and the two coordinate axes.

Which of the following is true of the above two statements?

Triangle ABCABC has vertices A=(5,6)A=(5, 6) and B=(6,3).B=(6, 3). If its area is 2222 and vertex CC lies on the line y=x+1y=x+1 in the first quadrant, what are the coordinates of C?C?

Given three points A=(1,0),B=(0,12),C=(k,k),\begin{array}{c}&A=(-1,0), &B=(0,12), &C=(k, k),\end{array} where k2,k\ge 2, what is the value of kk that minimizes the area of ABC?\triangle ABC?

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