Question

Someone please help me with these Geometry questions.

Answer 1

Answer: 112.5 square units

Work Shown:

A = area of the triangle

A = base*height/2

A = 9*7/2 = 63/2 = 31.5 ... see note1 below

B = area of rectangle

B = base*height

B = 9*3 = 27

C = area of parallelogram

C = base*height .... see note2 below

C = 9*6 = 54

If you're confused where I got the 6 from, check out the attached image below.

D = total area of the composite figure

D = A+B+C

D = 31.5 + 27 + 54

D = 112.5

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note1: The vertical component of the triangle is 9 units because this is part of the rectangle. The rectangle has opposite sides that are the same length. The parallelogram's vertical sides are 9 units long as shown by the single tickmark.

note2: a rectangle is essentially a special case of a parallelogram. In other words, a rectangle is a parallelogram with 4 right angles. So this is why the formula "area = base*height" shows up identical for both rectangles and parallelograms. Keep in mind that the height is always perpendicular to the base. You will not use the segments marked with double tickmarks.