Geometry Formulas and Calculations

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Questions and Answers

What is the slope-intercept form of a linear equation?

y=bx+m

y=m+b

y=mx+b (correct)

y=kx

In slope-intercept form, what does 'm' represent?

slope

In slope-intercept form, what does 'b' represent?

y-intercept

What is the formula for direct variation?

y=kx Signup and view all the answers

What is the formula to find the slope of a line between two points?

m = (y2 - y1) / (x2 - x1) Signup and view all the answers

What is the formula for the circumference of a circle?

C=2πr or C=πd Signup and view all the answers

What is the area formula for a triangle?

A=1/2bh Signup and view all the answers

What is the area formula for a rectangle or parallelogram?

A=bh Signup and view all the answers

What is the area formula for a trapezoid?

A=1/2(b1+b2)h Signup and view all the answers

What is the area formula for a circle?

A=πr² Signup and view all the answers

What is the lateral surface area formula of a prism?

S=Ph Signup and view all the answers

What is the lateral surface area formula of a cylinder?

S=2πrh Signup and view all the answers

What is the total surface area formula of a prism?

S=Ph+2B Signup and view all the answers

What is the total surface area formula of a cylinder?

S=2πrh + 2πr² Signup and view all the answers

What is the formula for the volume of a prism?

V=Bh Signup and view all the answers

What is the formula for the volume of a pyramid?

V=1/3Bh Signup and view all the answers

What is the formula for the volume of a sphere?

V=4/3πr³ Signup and view all the answers

What is the Pythagorean Theorem?

a² + b² = c² Signup and view all the answers

What is the formula for simple interest?

I=Prt Signup and view all the answers

What is the formula for compound interest?

A=P(1 + r)ᵗ Signup and view all the answers

Study Notes

Slope-Intercept Form

Equation is expressed as y = mx + b.
m represents the slope of the line.
b indicates the y-intercept where the line crosses the y-axis.

Direct Variation

Represented by the equation y = kx, where k is a constant.

Slope Calculation

Formula for the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

Circle Measurements

Circumference (C) can be calculated using C = 2πr (radius) or C = πd (diameter).
Area (A) of a circle is given by A = πr².

Triangle and Rectangle Measurements

Area of a triangle is calculated using A = 1/2 * base (b) * height (h).
Area of a rectangle or parallelogram is A = base (b) * height (h).

Trapezoid Area

The area of a trapezoid can be found using A = 1/2 * (b1 + b2) * height (h), where b1 and b2 are the lengths of the two parallel sides.

Prism and Cylinder Surface Areas

Lateral surface area of a prism is S = Perimeter of base (P) * height (h).
For a cylinder, lateral surface area is S = 2πr * height (h).

Total Surface Area Calculations

Total surface area of a prism is S = Ph + 2B, where B is the area of the base.
Total surface area of a cylinder is S = 2πrh + 2πr².

Volume Calculations

Volume of a prism is calculated using V = Base area (B) * height (h).
Volume of a pyramid is V = 1/3 * Base area (B) * height (h).
Volume of a sphere is given by V = 4/3πr³.

Pythagorean Theorem

Used to determine the relationship between the sides of a right triangle with the formula a² + b² = c², where c is the hypotenuse.

Interest Calculations

Simple interest (I) is calculated using I = Principal (P) * rate (r) * time (t).
Compound interest can be represented by the formula A = P(1 + r)ᵗ, where t is the number of compounding periods.

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Description

This quiz covers essential geometry formulas including slope-intercept form, circle measurements, and area calculations for various shapes such as triangles, rectangles, and trapezoids. Test your knowledge on how to apply these formulas effectively.