WAEC Mathematics 2017 Theory — Question 6

Model answer

Area of trapezium QTUS = Area of ΔTRU + Area of parallelogram QTRS. Area of parallelogram = base x height; the height is the same as that of ΔTRU, obtainable from Area(ΔTRU)=45=(1/2)x|RU|x|PS| → 45=(1/2)x10x|PS| → |PS|=9cm (the height). Area of parallelogram QTRS = |RS| x height = 6x9=54cm². Total area of trapezium QTUS = 45+54 = 99cm² (this can also be verified using Area=(1/2)(a+b)h where a=|SR|, b=|QT|, the two parallel sides).