Question

Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail 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.

a) 168sq. feet
b) 180sq. feet
c) 192sq. feet
d) 204sq. feet

Answer 1

To find the area of the parallelogram, decompose it into rectangles and triangles. The area can be calculated using the formula A = (3/2) * base * height. Assuming one value, the other can be found by solving the equation. The correct answer is d) 204 sq. feet.

Step-by-step explanation:

To calculate the area of the parallelogram, we can decompose it into rectangles and triangles. Let's call the base of the parallelogram 'b' and the height 'h'. Since opposite sides of a parallelogram are parallel and equal in length, we can form two rectangles by drawing a perpendicular line from one of the base points to the opposite side. This will divide the parallelogram into two equal triangles and two rectangles. The dimensions of the triangles will be b and h, and the dimensions of the rectangles will be b and h/2. Therefore, the area of the parallelogram is given by:

A = (b * h) + (b * h/2) = bh + bh/2 = 3/2 * bh

Given that the area of the parallelogram is 168 sq. feet, we can set up the equation:

168 = (3/2) * bh

Now we need to solve for b or h. Let's assume one of the values and find the other one. For example, let's assume the height is 12 feet:

168 = (3/2) * b * 12

336 = 3b

b = 336 / 3 = 112

Therefore, the base of the parallelogram is 112 feet. The area of the parallelogram is given by:

A = (3/2) * 112 * 12 = 2016 sq. feet

So the correct answer is d) 204 sq. feet.