Measurement And Geometry (9) Flashcards by Stephanie Geary

What is the formula for the perimeter of a rectangle?

Perimeter P = 2(l + w)

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Calculate the perimeter of a rectangle with length 8 cm and width 5 cm.

P = 2(8 + 5) = 26 cm

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What is the formula for the area of a rectangle?

Area A = l * w

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Calculate the area of a rectangle with length 8 cm and width 5 cm.

A = 8 * 5 = 40 cm²

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What is the formula for the area of a triangle?

A = 1/2 * base * height

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Calculate the area of a triangle with base 10 cm and height 6 cm.

A = 1/2 * 10 * 6 = 30 cm²

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What is the formula for the area of a parallelogram?

A = base * height

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Calculate the area of a parallelogram with base 12 cm and height 5 cm.

A = 12 * 5 = 60 cm²

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What is the formula for the area of a trapezoid?

A = 1/2 * (b1 + b2) * h

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Calculate the area of a trapezoid with bases 8 cm and 12 cm, height 5 cm.

A = 1/2 * (8 + 12) * 5 = 50 cm²

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What is the formula for the circumference of a circle?

C = 2πr

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Calculate the circumference of a circle with radius 7 cm.

C = 2 * π * 7 ≈ 43.98 cm

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What is the formula for the area of a circle?

A = πr²

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Calculate the area of a circle with radius 7 cm.

A = π * 7² = 49π ≈ 153.94 cm²

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What is the formula for the surface area of a rectangular prism?

SA = 2(lw + lh + wh)

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Calculate the surface area of a rectangular prism with length 5 cm, width 3 cm, height 4 cm.

SA = 2(15 + 20 + 12) = 94 cm²

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What is the formula for the volume of a rectangular prism?

V = l * w * h

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Calculate the volume of a rectangular prism with length 5 cm, width 3 cm, height 4 cm.

V = 5 * 3 * 4 = 60 cm³

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What is the formula for the surface area of a cylinder?

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SA = 2πr² + 2πrh

Calculate the surface area of a cylinder with radius 3 cm and height 10 cm.

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SA = 2 * π * 9 + 2 * π * 3 * 10 = 78π ≈ 245.04 cm²

What is the formula for the volume of a cylinder?

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V = πr²h

Calculate the volume of a cylinder with radius 3 cm and height 10 cm.

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V = π * 9 * 10 = 90π ≈ 282.74 cm³

What is the formula for the surface area of a sphere?

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SA = 4πr²

Calculate the surface area of a sphere with radius 6 cm.

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SA = 4 * π * 36 = 144π ≈ 452.39 cm²

What is the formula for the volume of a sphere?

V = 4/3 * πr³

Calculate the volume of a sphere with radius 6 cm.

V = 4/3 * π * 216 = 288π ≈ 904.78 cm³

Convert 2500 mL to litres.

2.5 L

Convert 3.2 km to metres.

3200 m

A polygon has 8 sides. What is the sum of interior angles?

Sum = (n - 2) * 180 = 1080°

Find the measure of each interior angle of a regular octagon.

Each = 1080° ÷ 8 = 135°

Two angles are supplementary. If one angle is 65°, what is the other?

115°

Two angles are complementary. If one angle is 40°, what is the other?

50°

A triangle has angles 50° and 60°. Find the third angle.

70°

Define sine in a right triangle and explain the variables.

sin(θ) = opposite/hypotenuse; θ = angle, opposite = side across from θ, hypotenuse = longest side

Define cosine in a right triangle and explain the variables.

cos(θ) = adjacent/hypotenuse; θ = angle, adjacent = side next to θ, hypotenuse = longest side

Define tangent in a right triangle and explain the variables.

tan(θ) = opposite/adjacent; θ = angle, opposite = side across from θ, adjacent = side next to θ

In a right triangle, θ = 30°, hypotenuse = 10 cm. Find the length of the side opposite θ using sine.

sin(30°) = opposite/10 → opposite = 10 * 0.5 = 5 cm

In a right triangle, θ = 45°, hypotenuse = 14 cm. Find the side adjacent to θ using cosine.

cos(45°) = adjacent/14 → adjacent = 14 * 0.707 ≈ 9.9 cm

A right triangle has θ = 60° and adjacent side = 8 cm. Find the opposite side using tangent.

tan(60°) = opposite/8 → opposite = 8 * √3 ≈ 13.86 cm

Solve a right triangle with hypotenuse = 10 cm and one leg = 6 cm. Find the other leg.

Use Pythagoras: other leg = √(10² - 6²) = √(100 - 36) = √64 = 8 cm

A ladder leans against a wall forming a 70° angle with the ground. If the base is 3 m from the wall, find the height the ladder reaches using tangent.

tan(70°) = height/3 → height = 3 * tan(70°) ≈ 8.19 m

A right triangle has sides 5 cm and 12 cm. Find the hypotenuse.

c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm

A building casts a shadow 20 m long. The angle of elevation of the sun is 30°. Find the height of the building.

tan(30°) = height/20 → height = 20 * tan(30°) ≈ 11.55 m

Explain how to choose which trigonometric ratio to use in a right triangle problem.

Identify the given side and the side you need; use sine if opposite & hypotenuse, cosine if adjacent & hypotenuse, tangent if opposite & adjacent

Solve for angle θ if opposite = 7 cm and hypotenuse = 10 cm.

sin(θ) = 7/10 = 0.7 → θ = arcsin(0.7) ≈ 44.4°

Solve for angle θ if adjacent = 5 cm and opposite = 12 cm.

tan(θ) = 12/5 = 2.4 → θ = arctan(2.4) ≈ 67.4°

A right triangle has legs 9 cm and 12 cm. Find all angles.

θ1 = arctan(9/12) = arctan(0.75) ≈ 36.87°, θ2 = 90 - 36.87 ≈ 53.13°, right angle = 90°

Measurement And Geometry (9) Flashcards

(47 cards)