Geometry Exercises: Arcs, Sectors, and Composite Shapes

Flashcards based on geometry exercises focusing on arc lengths, sector perimeters, and composite shapes.

What is the formula to find the arc length?

s = rθ, where r is the radius and θ is the angle in radians.

How do you convert degrees to radians?

Convert the angle from degrees to radians by multiplying by π/180.

What is the formula for the perimeter of a sector?

Arc Length + 2 * Radius

What is the arc length of a sector?

The length of the curved line forming the sector.

How to find the perimeter of a composite shape?

Sum of the lengths of all its sides.

What are composite shapes?

Shapes made up of a combination of basic shapes like rectangles, circles, and triangles.

What is the formula for the perimeter of a semicircle included in a shape?

πr + 2r, where r is the radius of the semicircle.

What does 'r' represent in geometric formulas?

The radius of the circle.

What is a sector of a circle?

A portion of a circle enclosed by two radii and an arc.

What is the radius of a circle?

A straight line from the center of the circle to any point on its circumference.

What is perimeter?

The distance around the outside of a shape.

How do you calculate the perimeter of a sector?

Add the length of the arc to twice the radius.

Describe the shape of the window mentioned in the exercise?

A window consisting of a rectangle and a Semicircle.

What is the formula for the circumference of a full circle?

P = 2πr

How to find the diameter if you know the radius?

Multiply radius by 2.

How do you find the radius of a circle if you only know the diameter?

Divide by 2.

What fraction of a circle is in the shape of a quadrant?

A quarter of a circle.

What is the exact perimeter formula of a quarter circle?

P = 2r + πr / 2

How is the arc length related to the central angle in a sector?

The angle is proportional to the fraction of the circle it covers.

How can the perimeter of a shape be found when using a diagram?

Adding individual sides to get to the total distance around the outside.