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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. (6 points)

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Sagot :

simplyniya2007

Answer:

 398 ft²

Step-by-step explanation:

Assuming you have correctly described the total area in terms of non-overlapping triangles and a rectangle, you can put the dimensions into the appropriate area formula and add up the pieces.

 Triangle area = 1/2·bh

 Rectangle area = bh

___

So, the first triangle has an area of ...

 1/2·(20 ft)(20 ft) = 200 ft²

The second triangle has an area of ...

 1/2·(6 ft)(6 ft) = 18 ft²

The rectangle has an area of ...

 (30 ft)(6 ft) = 180 ft²

And the area total is ...

 200 ft² +18 ft² +180 ft² = 398 ft²

The area of the polygon is 220.5 ft².

Given that, a six-sided polygon includes two isosceles right triangles, one with a height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet.

What are the formulas to find the area of triangle and rectangle?

The area of the triangle is 1/2×base×height and the area of the rectangle area is length×breadth.

The area of the first triangle is 1/2×15×15=112.5 ft².

The area of the second triangle is 1/2×4×4=8 ft²

The area of the rectangle is 25×4= 100 ft²

The total area=112.5+8+100=220.5 ft²

Therefore, the area of the polygon is 220.5 ft².

To learn more about the area of a rectangle visit:

https://brainly.com/question/12019874.

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