Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

mr. jones has a patio in the sahpe of a trapezoid. a round fountain having a circumference of 14 pi linear feet is placed in the corner as showin in the accompanying diagram. to the nearest square foot, how much of the patio s area ins not taken up by the fountanin? reall tha the circumferencie of a circle is calculated using c = 2

Sagot :

The area of the patio not taken up by the fountain is 241ft²

Please find attached an image of the patio

Area of the patio not taken up by the fountain = area of patio - area of fountain

The patio is in a shape of a trapezoid. Thus, the area of the patio can be determined by using the formula for the area of a trapezoid

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Characteristics of a trapezoid

  1. It has 4 vertices
  2. It has 4 edges
  3. If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram

Area of a trapezoid =  0.5 x (sum of the lengths of the parallel sides) x height

Taking a look at the image, we are not provided with the height of the trapezoid, just the parallel sides and the hypotenuse.

Pythagoras theorem can be used to determine the the height of the trapezoid

The Pythagoras theorem : a² + b² = c²

where a = height  

b = base = 20 ft - 12 ft = 8ft

8ft / 2 = 4

c =  hypotenuse

a² + 4² = 25²

a² = 625 - 16

a² = 609

√609 = 24.68 ft

Area of the trapezoid = 0.5 x (20 + 12) x 24.68 = 394.88 ft²

The fountain is in the shape of  a circle.

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius  

The radius would have to determined from the circumference

circumference of a circle = 2Ï€r

14Ï€ = 2Ï€r

r = 14Ï€ / 2Ï€

r = 7

Area of the circle = [tex]\frac{22}{7}[/tex] × 7²

[tex]\frac{22}{7}[/tex] × 49 = 154 ft²

Area of the patio not taken up by the fountain = 394.88 ft² - 154 ft² = 240.88ft²

To round off to the nearest square, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

The tenth digit is greater than 5, so one is added to 0. The number becomes 241ft²

Learn more about how to determine the area of a trapezoid here  : https://brainly.com/question/23814640?referrer=searchResults

View image ewomazinoade
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.