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

Welll....from the diagram, you can see you have two triangles (one on each side)

area of triangle = 1/2 base*height = 1/2 * 2 x 15 = 15ft2 each then you are left with a rectangle 13 ft x 15= 195 ft2

195+15+15=

225 ft2 <----- ANSWER

Answer 2

The area of the parallelogram is equal to 300 square feet.

Given the following data:

• Width of parallelogram = 20 feet.

• Base of triangle = 4 feet.

• Height of triangle = 15 feet.

To calculate the area of the parallelogram:

First of all, we would determine the area of the triangles.

Note: There are two (2) triangles that can be cut-off the given parallelogram.

The formula for the area of a triangle.

Mathematically, the area of the triangle is given by the formula:

$Area=\frac{1}{2} \times base \times height\\\\Area=\frac{1}{2} \times 4 \times 15\\\\Area=2 \times 15$

Area = 30 $ft^2$

For the two (2) triangles:

$Area = 2 \times 30$

Area = 60 $ft^2$

For the rectangle left:

• Length = 15 ft.

• Width = 20 - 4 = 16 ft.

$Area = length \times width\\\\Area = 15 \times 16$

Area = 240 $ft^2$

Now, we can calculate the area of the parallelogram:

$Area \;of \;parallelogram = 60 + 240$

Area of parallelogram = 300 $ft^2$

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