<h3>Given</h3>
1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.
2) Regular pentagon PENTA with side lengths 9 m
<h3>Find</h3>
The area of each figure, rounded to the nearest integer
<h3>Solution</h3>
1) The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
Answer:
less than 2,000 times wider
Step-by-step explanation:
The height of the tree is 60 meters.
Explanation:
Let the height of the tree be x. The tree casts a shadow of 
meters and the distance from the top of the tree to the end of the shadow is 
meters.
The sides of the triangle are attached in the image below:
Using pythagoras theorem,
Expanding, we get,
Solving the equation using the quadratic formula 
, we get,
Simplifying, we have,
Thus,
and 
where the value 
is not possible because substituting the value in results in negative solution. Which is not possible.
Hence, the value of x is 60.
Thus, The height of the tree is 60 meters.
