find the area of the pentagon in the diagram below.
15 square inches
20 square inches
25 square inches
28 square inches
Answers
The area of the pentagon is approximately 15 square inches.
To find the area of the pentagon, we can use the formula for the area of a regular pentagon:
Area = (5/4) * (s²) * (1/tan(π/5)),
where "s" is the length of the side of the pentagon.
Given that the sides of the pentagon are as follows:
Two smallest sides = 2 inches,
Two largest equal sides = 4 inches,
One other equal side = 3 inches.
Since the pentagon is not a regular pentagon, we need to find the area by dividing it into different shapes and then calculating their individual areas.
The pentagon can be divided into three shapes: a rectangle and two triangles.
Rectangle:
The two smallest sides (2 inches) form the length and width of the rectangle.
Area of the rectangle = Length * Width = 2 inches * 2 inches = 4 square inches.
Triangle 1:
The two largest equal sides (4 inches) and one of the 3-inch sides form a triangle.
To calculate the height (h) of the triangle, we can use the Pythagorean theorem, since it is a right triangle.
h² = (4 inches)² - (1.5 inches)², [1.5 inches is half of the 3-inch side]
h² = 16 inches² - 2.25 inches²,
h² = 13.75 inches²,
h ≈ 3.7 inches.
Area of Triangle 1 = (1/2) * Base * Height = (1/2) * 3 inches * 3.7 inches ≈ 5.55 square inches.
Triangle 2:
The two largest equal sides (4 inches) and the other 3-inch side form another triangle.
Using the same height (3.7 inches) from Triangle 1:
Area of Triangle 2 = (1/2) * Base * Height = (1/2) * 3 inches * 3.7 inches ≈ 5.55 square inches.
Now, to find the area of the pentagon, we add the areas of the rectangle and the two triangles:
Total Area = Area of Rectangle + Area of Triangle 1 + Area of Triangle 2
Total Area = 4 square inches + 5.55 square inches + 5.55 square inches
Total Area ≈ 15.1 square inches.
Therefore, the area of the pentagon is approximately 15.1 square inches.
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Step-by-step explanation:
Since the rectangle is divided into 8 equal parts and two parts are shaded, this simply means that 2 out of 8 parts are shaded which is 2/8.
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Step-by-step explanation:
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Step-by-step explanation:
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a Write her rate of pay per hour,
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Answers
B)12 * 7
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A.
66
B.
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C.
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D.
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Answers
Answer:
B. 66
Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
45 inches
Step-by-step explanation:
C = (pi)(diameter).
Assuming that the radius of the pizza in this case is 7 inches, the diameter is twice that, or 14 inches.
Thus, the circumference of the pizza is C = (3.14)(14 inches) = 45 inches
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Answers
Step-by-step explanation:
Because to make a triangle you have to add up all the sides and they make 180 no matter what and if you add 60,100,and 40 it will pass 180.
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Answers
Answer: [tex]x+3[/tex]
Step-by-step explanation:
Given
[tex](x+5)[/tex] is a factor of [tex]x^2+8x+15[/tex] , that is
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Step-by-step explanation:
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Answers
The question is incomplete:
A business shipped 106 packages one day. Customers are charged 4.50 for each standard delivery and 7.50 for each express delivery. Total shipping charges for the day were $600.00. How many of each kind of package were shipped?
Answer:
The business shipped 65 standard delivery packages and 41 express delivery packages.
Step-by-step explanation:
Since the business shipped 106 packages one day you can say that:
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Answers
Answer:
249 brownies in each bag.
Step-by-step explanation:
I know this because 332x15=4,980
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Answers
Answer:
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Step-by-step explanation:
Given
[tex]\sin(x + 4) = \cos(3x)[/tex]
Required
Find [tex]\tan(x + 40)[/tex]
In trigonometry
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[tex]\tan(x + 40) = \tan(21.5+40)[/tex]
[tex]\tan(x + 40) = \tan(61.5)[/tex]
Using a calculator:
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Mean = 69Median = 69Mode = {68, 70}===============================================
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-------
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Repeat the process of crossing off the smallest and largest items to get {68, 68, 70, 70}. Do so one more time and we get {68,70}.
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--------
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Step-by-step explanation:
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Answers
Step-by-step explanation:
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Answers
Answer:
3 |3 - 5x| - 8= -8
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Answer:
one solution at 0.6
Step-by-step explanation:
3|3-5x| = 0
|3-5x| = 0
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Please help and also include an explanation so I know how you got the answer.
Answers
Answer:
x = 15
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
I gotcha bro
The line C is straight and straight lines are 180°
so 180° = 4x + 8x = 12x ----> 180 = 12x ---> then divide both sides by 12
180/12 = 15 and 12x/12 = x
so 15 = x or x = 15