Quadrilaterals
What is the formula for the area of a parallelogram?
Answer: Area = base × height.
How can you find the area of a composite figure?
Answer: Decompose it into familiar shapes, find the area of each shape, and add them all together to find the total area of the composite figure.
What is a scale drawing?
Answer: A representation that shows an object reduced or enlarged by a specific ratio.
What is the formula for the circumference of a circle?
Answer: Circumference = 2πr, where r is the radius.
What is the formula for finding the surface area of a right circular cylinder?
Answer: Surface Area = 2πr2 + 2πrh, where r is the radius and h is the height.
How do you find the area of a trapezoid?
Answer: Area = 1/2×(b1+b2)×h, where b1 and b2 are the lengths of the bases and h is the height.
If a composite figure consists of a rectangle (length = 8 cm, width = 3 cm) and a triangle (base = 3 cm, height = 4 cm), what is the total area?
Answer: Area = 24 cm² (rectangle) + 6 cm² (triangle) = 30 cm².
If a drawing of a house is 3 cm wide and the scale is 1 cm = 4 m, how wide is the actual house?
Answer: Actual width = 3 cm × 4 m/cm = 12 m.
If a circle has a diameter of 10 cm, what is its circumference?
Answer: Circumference = 2π • 5 = 10π cm ≈ 31.4 cm.
If a cylinder has a radius of 2 cm and a height of 5 cm, what is its surface area?
Answer: Surface area = 2π • 22 + 2π • 2 • 5 ≈ 87.96 cm2
A rhombus has a base of 10 1/2 in and a height of 10 in. What is its area?
Answer: A = 10.5 • 10 = 105 in2
What formulas would you need to find the area of a composite figure that included a trapezoid and a parallelogram?
Answer: Area = 1/2 • (b1 + b2) • h (trapezoid) + b • h (parallelogram).
How do you find the scale factor between a drawing and the actual object?
Answer: Divide the actual measurement by the drawing measurement.
How do you find the area of a circle?
Answer: Area = πr2, where r is the radius.
How can you find the volume of a right circular cylinder?
Answer: Volume = πr2h
A parallelogram has a base of 15 cm and a height of 3.2 cm. What is its area?
Answer: A = 15 • 3.2 = 48 cm2
A composite figure is made of a square (side = 4 cm) and a semicircle (diameter = 4 cm). What is the total area?
Answer: Area = 16 cm² (square) + 6.28 cm² (semicircle) = 22.28 cm².
A scale drawing of a patio is 1:100. If the drawing is 5 cm long, how long is the actual patio?
Answer: Actual length = 5 cm × 100 = 500 cm or 5 m.
A circle has a radius of 3 cm. What is its area?
Area = π•32 = 9π cm² ≈ 28.27 cm².
A cylinder has a radius of 4 ft and a height of 10 ft. What is its volume?
Answer: Volume = π • 42 • 10 = 160π cm3 ≈ 502.65 cm³
How do the areas of a rhombus and a parallelogram with the same base and height compare?
Answer: They are equal.
A figure is composed of a rectangle, a triangle, and a semi-circle. The base of the rectangle is 3 ft and the height is 3 ft. The triangle has a base of 3 ft and a height of 6 ft. The semi-circle has a radius of 4 ft. What is the area of the composite figure?
Answer: A = (3 • 3) + (0.5 • 3 • 6) + (0.5 • 3.14 • 42) = 43.12 ft2
What is the importance of using scale factors in architecture?
Answer: Scale factors allow for accurate representations of large structures in a manageable size.
Explain the relationship between the circumference and diameter of a circle.
The ratio of circumference to diameter is always equal to π (pi).
Discuss a real-world application of calculating the surface area of a cylinder.
Answer: Surface area calculations are used in manufacturing cans or pipes to determine the amount of material needed.