Podcast
Questions and Answers
Using Euler's Theorem, how many edges does a solid with 11 faces and 11 vertices have?
Using Euler's Theorem, how many edges does a solid with 11 faces and 11 vertices have?
What is the surface area of a salad bowl with a radius of 8.9 inches, assuming it is half a sphere?
What is the surface area of a salad bowl with a radius of 8.9 inches, assuming it is half a sphere?
How much would it cost to wrap an 8.5-inch cube box with wrapping paper costing $0.025 per square inch?
How much would it cost to wrap an 8.5-inch cube box with wrapping paper costing $0.025 per square inch?
Which sporting ball is expected to have a smaller surface area, a golf ball or a tennis ball?
Which sporting ball is expected to have a smaller surface area, a golf ball or a tennis ball?
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What is the surface area of a round sea turtle egg with a diameter of 0.5 cm?
What is the surface area of a round sea turtle egg with a diameter of 0.5 cm?
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Which method is used to calculate the perimeter of the triangle with side lengths using trigonometric ratios?
Which method is used to calculate the perimeter of the triangle with side lengths using trigonometric ratios?
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How is the area of a regular pentagon calculated when divided into triangles?
How is the area of a regular pentagon calculated when divided into triangles?
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In the given problem involving hauling chairs, what is the total area of the two chairs?
In the given problem involving hauling chairs, what is the total area of the two chairs?
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What is the formula for the area of a sector in a circle?
What is the formula for the area of a sector in a circle?
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What is the perimeter of the rectangle if the length is 8 cm and the width is 4 cm?
What is the perimeter of the rectangle if the length is 8 cm and the width is 4 cm?
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What does the term $\frac{n}{360^\circ}$ represent when calculating the area of a sector?
What does the term $\frac{n}{360^\circ}$ represent when calculating the area of a sector?
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How is the area of a segment of a circle defined?
How is the area of a segment of a circle defined?
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What is the formula for calculating the area of a triangle?
What is the formula for calculating the area of a triangle?
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If the density of objects in an area is 10 objects per square unit and there are 200 objects, what is the area of the figure?
If the density of objects in an area is 10 objects per square unit and there are 200 objects, what is the area of the figure?
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In a solid figure with 14 vertices and 21 edges, what is the number of faces?
In a solid figure with 14 vertices and 21 edges, what is the number of faces?
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Study Notes
Area Module Review
- Problem 1: A triangle with angles 45°, 45°, and 90°, and one side of length 4.9 units. Find perimeter. Special Right Triangle Theorem or trigonometry used to find the lengths of the other sides. Perimeter = 16.7 units.
Problem 2
- A triangle with vertices (3, -1), (9, -5), and (16, -2). Perimeter calculated using distance formula. Perimeter is 27.9 units.
Problem 3
- A rectangle with vertices (11, 0), (11, 5), (17, 5), and (17, 0). Perimeter calculated by finding lengths of sides using the distance formula. Perimeter = 22 units.
Problem 4
- A right triangle with a 51.3° angle. Explain how to find the perimeter. Use trigonometric ratios (tangent and cosine of 51.3 degrees) to compute unknown side lengths, then add to get perimeter.
Problem 5
- A polygon with four triangles. Find the area of the polygon. Triangles with base 8 cm and heights 4 cm and 6 cm calculated separately. Total Area = 40 cm2
Problem 6
- A regular pentagon divided into five congruent triangles. Find the area. Area formula for a regular pentagon is perimeter times half the apothem. Area = 120 cm2.
Problem 7
- Find the area of a polygon on a coordinate plane. Divide into a rectangle and two triangles to find the area. Total area is 16 square units.
Problem 8
- A family wants to haul two chairs (3 ft wide, 4 ft high) in a truck (5 ft wide, 8 ft long). Determine if both chairs will fit at the same time. Calculated area of the vehicle and chairs to show they will fit.
Problem 9
- Area of a sector formula: Asector = (n/360)πr2. Identify what the variable n represents. n is the central angle of the sector.
Problem 10
- Area of a sector formula: Asector = (n/360)πr2. Identify what the term n/360 represents. The term n/360 represents the ratio of the sector's central angle to the circle's total angle.
Problem 11
- Definition of a segment of a circle. A segment of a circle is a portion of a sector bounded by a chord and the minor arc formed by that chord.
Problem 12
- Find the area of a minor sector AOB. Given a circle with a sector AOB having a central angle of 215 degrees. A radius that is 3.2 units long. Calculation to find the area of the sector is shown. Area = 13 square units.
Problem 13
- Equation for calculating the area of a triangle: A = ½ (base × height).
Problem 14
- Density problem. Calculate the total number of men if there are 100 men per city block and 2000 blocks in the city. 100 men / city block * 2000 city blocks = 200,000 men.
Problem 15
- Density problem. Given 10 objects/sq unit and 200 objects, determine area. 200 objects /10 objects/sq unit = 20 sq units.
Problem 16
- Multiple methods for calculating the area of an unknown figure: Divide into known shapes, use context, or use density of objects in a figure to determine the area.
Problem 17
- Count faces, vertices, and edges of a figure. Faces = 7, vertices = 7, edges = 12.
Problem 18
- Euler's Theorem. Find the number of faces in a solid with 14 vertices and 21 edges. F + V = E + 2 --> F + 14 = 21 + 2 --> F = 9
Problem 19
- Is the shape a polyhedron? Explain. No, a curved side disqualifies a shape as a polyhedron. Polyhedrons consist only of straight sides.
Problem 20
- Euler's Theorem. Find the number of edges in a solid with 11 faces and 11 vertices. F + V = E + 2 --> 11 + 11 = E + 2 --> E = 20
Problem 21
- Wrapping paper cost of a box. A box with sides of 8.5 inches. The surface area of the box is 433.50 square inches. Cost = $10.84.
Problem 22
- Surface area of a salad bowl. A semi-sphere with a radius of 8.9 inches. Calculate the surface area. 497.44 square inches.
Problem 23
- Comparing surface area of a golf ball and tennis ball. Without diameters, a golf ball has a smaller surface area. The smaller the radius, the smaller the surface area will be in the formula SA=4(π)(r2)
Problem 24
- Surface area of a sea turtle egg. A round sea turtle egg measuring 0.5 cm in diameter. Calculate the surface area. 0.79 square cm.
Problem 25
- Surface area of a regular pyramid. Formula (½)P(L) + B.
Problem 26
- Surface area of a cone. Formula S = πr(l+r).
Problem 27
- Surface area of a cone. Formula S = πr(l+r) use Pythagorean theorem to determine the slant height. Area = 36π m2.
Problem 28
- Surface area of a regular pyramid. Given a pyramid shape. Calculate surface area using the formula S = (½)PL+B, where P is the perimeter of the base and L is the slant height.
Problem 29
- Surface area of a rectangular prism. A rectangular prism with a height of 16 ft, a width of 10 ft, and a length of 13 ft. Calculate the surface area using the formula SA = 2B+PH. 996 square feet.
Problem 30
- Surface area of a cube. A cube with a side length of 8 meters. SA = 2B + PH. Surface area = 384 m2
Problem 31
- Surface area of a triangular prism, SA = 2B + ph. Calculate the surface area. Area = 205.9 cm2
Problem 32
- Surface area of a rectangular prism, SA = 2B + ph. Calculate the surface area. Area = 2698 ft2
Problem 33
- Conversion factor from meters to millimeters. There are 1,000 millimeters in a meter.
Problem 34
- Area conversion from meters squared to millimeters squared. Multiply by 1,000,000.
Problem 35
- Area conversion factor. Square the conversion factor if dealing with an area measurement.
Problem 36
- Conversion factor from meters squared to inches squared. Show work for each step to convert from meters squared to inches squared. Conversion factor calculated in previous example.
Problem 37
- Formula for calculating the area of a pyramid. Area = (½) (perimeter base)(slant height)+area of base.
Problem 38
- Dimension decrease effect on area. Decreasing a dimension decreases the area.
Problem 39
- Surface area of a building. A rectangular building with dimensions 7 meters by 7 meters and a height of 6 meters. The surface area is 245 square meters.
Problem 40
- Mistake in calculating water needed to spray a building. Calculate surface area of a building/cube without area of the bottom. The calculation of the surface area of a building must not include the base of the building.
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Description
Test your knowledge on calculating perimeters and areas of various geometric shapes including triangles, rectangles, and polygons. This quiz will cover key concepts including the Special Right Triangle Theorem, distance formula, and trigonometric ratios. Perfect for reinforcing your understanding of geometry!
