31/8 as a mixed number is :
Jimmy made 16 quarts of lemon juice. How many liters of lemon juice did Jimmy make? 1 gallon = 4 quarts 1 gallon = 3.785 liters
2 answers:
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<u>Given:</u>
A triangular piece is cut out of a rectangular piece of paper to make the class banner.
<u>To find:</u>
The area of the class banner.
<u>Solution:</u>
The rectangular piece of paper is 14 inches long and inches wide.
From the given diagram, the triangle has a base length of the same 8 inches and has a height of inches long.
To determine the area of the banner, we subtract the area of the triangle from the area of the rectangle.
The area of a triangle
The area of the triangle square inches.
The area of a rectangle
The area of the rectangle square inches.
The area of the class banner square inches.
So the banner has an area of 100 square inches which is the first option.
9514 1404 393
Answer:
1) 135°
2) 0.77 units
3) 0.92 units
4) 6.12 units
5) 2.83 square units
Step-by-step explanation:
1) The exterior angle at any vertex is 360°/n, where n is the number of sides. For the octagon, the exterior angle is 360°/8 = 45°. The interior angle will be the supplement of this: 180° -45° = 135°.
The measure of each interior angle is 135°.
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2) Each sector of the octagon is an isosceles triangle with a central angle of 45° (also 360°/8). Since the radius is 1 unit, the length of one side is twice the sine of half the central angle.
s = 2·sin(45°/2) ≈ 0.765367
The length of one side is about 0.77 units.
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3) Similarly, the apothem is the cosine of half the central angle:
a = cos(45°/2) ≈ 0.923880
The apothem is about 0.92 units.
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4) For an octagon, the perimeter is 8 times the length of one side.
P = 8s = 8(0.765367) ≈ 6.12293
The perimeter is about 6.12 units.
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5) The area of one sector (isosceles triangle) is given by the formula ...
A = (1/2)bh
A = 1/2sa ≈ 1/2(0.765367)(0.923880) ≈ 0.353553
Then the area of the octagon is 8 times this:
A = 8(sector area) = 8(0.353553) ≈ 2.82843
The octagon area is about 2.83 square units.
