Draw and classify the polygon with the given vertices. Find the perimeter and the area of the polygon. M(-2,5), N(3,-2), P(-2,-2
)
2 answers:
Answer:
- see below for a drawing
- right triangle
- perimeter = 20.6 units
- area = 17.5 units²
Step-by-step explanation:
A graph shows the figure to be a right triangle with a base of 5 units and a height of 7 units. Its hypotenuse will be given by the Pythagorean theorem:
MN² = MP² +PN²
MN² = 7² +5² = 74
MN = √74 ≈ 8.60
__
The perimeter is the sum of the side lengths:
Perimeter = MN +MP +PN = 8.60 +7 +5
Perimeter = 20.60 . . . . units
__
The area is given by the area formula:
Area = 1/2bh = 1/2·5·7 = 35/2
Area = 17.5 . . . . square units
The polygon is a right triangle with a perimeter of 20.60 units and an area of 17.5 square units
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Answer:
80 m²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = h (a + b)
where h is the perpendicular height between bases and a, b are the bases
Here h = 8, a = 14 and b = 6, thus
A = × 8 × (14 + 6) = 4 × 20 = 80 m²
Answer:
George is 43.20 ft East of his starting point.
Step-by-step explanation:
Let Paula's speed be x ft/s
George's speed = 9 ft/s
Note that speed = (distance)/(time)
Distance = (speed) × (time)
George takes 50 s to run a lap of the track at a speed of y ft/s
Meaning that the length of the circular track = y × 50 = 50y ft
George and Paula meet 14 seconds after the start of the run.
Distance covered by George in 14 seconds = 9 × 14 = 126 ft
Distance covered by Paula in 14 seconds = y × 14 = 14y ft
But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track
That is,
126 + 14y = 50y
50y - 14y = 126
36y = 126
y = (126/36) = 3.5 ft/s.
Hence, Paula's speed = 3.5 ft/s
Length of the circular track = 50y = 50 × 3.5 = 175 ft
So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of
9 × 240 = 2160 ft.
2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.
Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft
So, 60 ft along a circular track subtends an angle θ at the centre of the circle.
Length of an arc = (θ/360°) × 2πr
2πr = total length of the circular track = 175
r = (175/2π) = 27.85 ft
Length of an arc = (θ/360) × 2πr
60 = (θ/360°) × 175
(θ/360°) = (60/175) = 0.343
θ = 0.343 × 360° = 123.45°
The image of this incomplete lap is shown in the attached image,
The distance of George from his starting point along the centre of the circular track = (r + a)
But, a can be obtained using trigonometric relations.
Cos 56.55° = (a/r) = (a/27.85)
a = 27.85 cos 56.55° = 15.35 ft
r + a = 27.85 + 15.35 = 43.20 ft.
Hence, George is 43.20 ft East of his starting point.
Hope this Helps!!!
