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Answer:
y = 1/2x + 5
Step-by-step explanation:
Given :
Slope, m = 1/2
(x1, y1) = (6, 8)
y - y1 = m(x - x1)
y - 8 = 1/2(x - 6)
y - 8 = 1/2x - 3
y - 8 + 8 = 1/2x - 3 + 8
y = 1/2x + 5
Stamdard form of equation :
y = mx + c
Hence, equation is :
y = 1/2x + 5
<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.
