Question

Bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area of the polygon. Be sure to show all your work and explain your answer.

Six-sided polygon that includes two isosceles right triangles, one with height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet (Picture Below).



Could you please write out an actual paragraph or detailed steps? I would prefer that, since I have to write a paragraph. Thank you!

Answer 1

The answer is 220.5

Explanation:

This shape is an irregular polygon. This means we have to find the area of the whole shape and then subtract the missing parts to get the correct answer.

First, we have to find the area of the whole shape (a rectangle). The formula for a rectangle's area is:

L x W

The length of the shape is 19 ft, and the width is 29 ft. Now, we apply the formula to those numbers:

19ft x 29 ft = 551 square feet

Now that we know that the area of the whole polygon is 551 square feet, we have to find the area of:

1. The first missing triangle

2. The second missing triangle

3. The missing rectangle

Add all of those areas together, and then subtract them from 551 and we have the answer.

First, we find the area of the missing triangle in the top left hand corner. The area formula for a triangle is:

1/2 x b x h

So, we have to find the base and the height. We see that part of the whole polygon's width is 4 ft, which is not missing, so we subtract that from the total width, 19 ft.

19 - 4 = 15

This means that the triangle's base is 15 ft. Now, we have to find the height. We can easily see that the height is 15 ft, as it says so in the picture.

Now, we just have to apply the formula:

1/2 x 15ft x 15ft = 112.5 square feet

So, we have our first area, 112.5 square feet.

Now we have to find the area of the second missing triangle in the bottom right corner.

We know that the base is 4 ft, as it says so in the picture. The height is 24 ft. We know that the total height of the polygon is 29 ft, and we see a shaded part of 25 ft in height. So:

29 - 25 = 4

According to this equation, we have 4 ft in height. Using the area formula for triangles, here is our equation:

This equation states that our second area is 8 square feet.

1/2 x 4ft x 4ft = 8ft

Now, we just have our last area to find, the missing rectangle. According to all of the previous information, and the picture, we see that the width is 15 ft and the height is 14 ft. Now we apply the area formula for rectangles:

15ft x 14 ft = 210 square feet

Lastly we add up all of our areas: 112.5 square feet, 8 square feet, and 210 square feet.

112.5ft + 8ft + 210ft = 330.5 square feet

Then, we subtract 330.5 from 551:

551 - 330.5 = 220.5

The answer is 220.5

Answer 2

To calculate the area of a Hexagon you could find how many right triangles are in the hexagon and calculate the area of those right triangles to the amount of right triangles there are in the hexagon. A Hexagon has 6 isosceles triangles with bases of 15 ft and height of 4 ft, which means it has 12 right triangles with base of 7.5 and height of 4ft,. Area of the right triangle is bh/2 (base times height divided by two) which base is 7.5 and height is 4 so bh=30 and divided by two is 15, there are 12 right triangles so you can multiply 15*12 and that's the area of the Hexagon which is 180 degrees

~SharkieOwO~