Area and Properties of Polygons

Area and Properties of Polygons

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to calculate the area of an inscribed regular 2n-gon within a circle by decomposing it into triangles. It then introduces an inscribed regular n-gon and derives a formula for the area of the 2n-gon. As n approaches infinity, the polygons approximate the circle, leading to the derivation of the circle's area formula as πR².

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial shape used to start the process of finding the area of the inscribed polygon?

A rectangle

A circle

A triangle

A square

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial step in finding the area of the inscribed 2n-gon?

Drawing a hexagon

Drawing a triangle

Drawing a circle

Drawing a square

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the regular 2n-gon decomposed to find its area?

Into squares

Into circles

Into triangles

Into hexagons

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the side length of the inscribed regular n-gon denoted as?

T

P

S

R

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the base length of the triangle used in the area calculation of the 2n-gon?

2R

R

S/2

S

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the height of the triangle used in the area calculation of the 2n-gon?

R/2

S/2

R

S

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the role of the radius R in the area calculation of the 2n-gon?

It is the perimeter of the n-gon

It is the side length of the n-gon

It is the base of the triangle

It is the height of the triangle

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