1. Vertices are A(-1,0), B(5,-3), C(-1,-6), D(-7,-3), P(-4.6,1.8)base AB = sqrt[ {5-(-1)}^2 + (-3-0)^2 ] = sqrt ( 36 + 9 ) = 6.71 unitsheight DP = sqrt[ { -4.6 -(-7)}^2 + {1.8-(-3) }^2 ] = sqrt (5.76 +18.44) = 5.92 unitsSo the area of rhombus ABCD = base AB x height DP = 6.71 x 5.92 = 39.72 units^22. Vertices are A(-4,9), B(11,9), C(5,-1), D(-10,-1)a = AB = ( 11-(-4), 9-9 ) = ( 15, 0)b = AC = ( -1 -(-4), -6-9) = ( 3, -15)Area of the parallelogram is the cross product of a and bArea of the parallelogram ABCD is = a x b = ( 15, 0) x ( 3, -15) = (15*-15 - 0*3) = 225 units^23. Vertices are A(-2,2), B(2,5), C(11,-7), D(1,-2)AB = sqrt[ {2-(-2)}^2 + (5-2)^2 }] = 5 unitsAD = sqrt[ {1-(-2)}^2 + (-2-2)^2 }] = 5 unitsBC = sqrt[ (11-2)^2 + (-7-5)^2 }] = 15 unitsIN the trapezoid ABCD, AD and BC are two parallel sides and AB side is the heightSo area = [ (AD+BC)/2] * AB = [ (5+15)/2] *5 = 50 units 4. The figure is confined in max area = 8 * 8 = 64 small squares = 64 ft^2The total uncut squares inside the figure = 34 small squares = 34 ft^2There are also about 18 half squares inside the figureSo the area of the figure is best estimated of 50ft^25. There are 8 units on x axis from 0.5 to 4.5and 4 units on y axis under min point of the curveArea under the min point of the curve = 8*4 = 32 units^2Between the max and min point of the curve there are about 8*1/2 = 4 units^2Total area = 32 + 4 = 36 units^2Thus best describes the area under the curve is 35 units^2