What are the missing angle in parallelogram rstu
1 answer:
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Answer:
117
Step-by-step explanation:
First think of the square that was removed. All 4 sides are equal but you don't know the length so lets gives them the variable X.
So to find the area of the rectangle, insert those variables into the area equation for a rectangle.
(RV + (X) ) (PT +(X)) = rectangle area
Now you are given what the area is if you remove the square. So subtract the the square's area from the equation above and set it equal to the size they told you.
(RV + (X)) (PT + (X)) - [(X)(X)] = 92
rectangle - square = remaining area
Now plug in the numbers you know and solve for X.
(8 + X) (4 + X) - ((X)(X)) = 92
Use FOIL to multiply the first part of the equation (first, outer, inner, last)
32 + 8x + 4x + -
= 92
32 + 12x = 92
12x = 60
x = 5
So now you know the size of the square. Each side is 5m. So add 5m onto the top of the rectangle and onto the side. The top is 13m and the side is 9m. The area of the rectangle is the length times the height to 13 x 9 which is 117
Answer:
Area of the regular dodecagon inscribed in a circle will be 27 square units.
Step-by-step explanation:
A regular dodecagon is the structure has twelve sides and 12 isosceles triangles inscribed in a circle as shown in the figure attached.
Since angle formed at the center by a polygon =
Therefore, angle at the center of a dodecagon = = 30°
Since one of it's vertex is (3, 0) therefore, one side of the triangle formed or radius of the circle = 3 units
Now area of a small triangle =
where a and b are the sides of the triangle and θ is the angle between them.
Now area of the small triangle =
=
Area of dodecagon = 12×area of the small triangle
= 12×
= 27 unit²
Therefore, area of the regular octagon is 27 square unit.
