Question

Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work.

Answer 1

Answer:

Area of parallelogram is 150 square ft

Step-by-step explanation:

Given the parallelogram in the figure whose height is 10 ft and base length is 15 ft.

Area of parallelogram is $base \times height$

                                       = $15\times 10ft^2$

                                       = 150 square ft

now we have to decompose this parallelogram into rectangles and triangles and then to determine the shape.

The given parallelogram KLMN can be decomposed into 2 triangles and one rectangle.

2 right angled triangles KPL and NOM by construction

$KL^{2}=KP^{2}+PL^{2}=10^{2}+2^{2} =100+4=104$

⇒ $KL=\sqrt104=10.2 ft=MN$         (∵ KLMN is a parallelogram)

Hence, dimension of triangles are 10 ft, 2 ft and 10.2 ft

Now rectangle KPON with dimension 15 ft and 10 ft because KP and NO are perpendiculars on LM.