Find the area of a polygon

The area of a polygon is the measure of the amount of surface it encloses. Area is measured in square units, such as square inches or square centimeters

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QUESTION OF
Views #: 28
Questions #: 21
Time: 20 minutes
Pass Score: 80.0%
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Area of a Right Triangle

1 pts
volume_mute

Find the area of the right triangle shown below.

b = 11 cma = 15 cm
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Area of a Parallelogram

1 pts
volume_mute

Calculate the exact area of the parallelogram provided below.

h = 8 mb = 16 m
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Area of an Isosceles Trapezoid

1 pts
volume_mute

Find the total interior area of the trapezoid depicted in the diagram.

h = 6 ftb₁ = 10 ftb₂ = 18 ft
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Area of a Rhombus

1 pts

A rhombus has diagonal perpendicular lengths of \(d_1 = 14\text{ cm}\) and \(d_2 = 22\text{ cm}\). Calculate its area.

Answer = (1)

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Missing Dimension from Area

1 pts
volume_mute

A triangle has a calculated total area of \(48\text{ m}^2\). If its horizontal base measures \(12\text{ m}\), find its vertical altitude height.

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Area of a Regular Hexagon

1 pts

Match the components of a regular hexagon with a side length of \(s = 8\text{ units}\) and an apothem of \(a \approx 6.93\text{ units}\) to its properties.

To complete the line match

  1. Click on an item in the first group
  2. Click on the match in the second group

To delete a match, double click on a line

Properties

Perimeter
Total Area

Values

48 units
166.32 sq units
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Explanation

Properties of Regular Polygons

1 pts

Classify the following geometric descriptions with respect to their area characteristics for regular polygons.

drag and drop the selected option to the right place

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Area of a Regular Pentagon

1 pts

A regular pentagon has an apothem length of \(5.5\text{ in.}\) and a single side length of \(8\text{ in.}\). Find its complete area.

Answer = (1)

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Area of a Kite

1 pts
volume_mute

Find the total surface area of a geometric kite whose main diagonal lines measure \(12\text{ cm}\) and \(17\text{ cm}\).

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Area of a Composite Shape

1 pts
volume_mute

Find the total combined area of the composite region made up of a rectangle and a right triangle.

10 cm8 cm5 cm
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Apothem Theorem Verification

1 pts
volume_mute

True or False: The apothem of a regular polygon always meets the side to which it is drawn at a right angle (90 degrees).

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Area of an Equilateral Triangle

1 pts

Using the specific polygon rules, identify the missing word in the definition placeholder space:

A straight line segment segment connecting the geometric center of a regular polygon to any outer corner vertex is named the (1).

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Trapezoid Height Extraction

1 pts
volume_mute

A trapezoid possesses parallel bases of \(b_1 = 9\text{ m}\) and \(b_2 = 15\text{ m}\). If its computed area is exactly \(72\text{ m}^2\), what is its vertical height?

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Area of a Regular Octagon

1 pts

A regular 8-sided octagon features an apothem of \(12\text{ cm}\) and a single edge boundary line of \(10\text{ cm}\). Find the total area.

Answer = (1)

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Comparing Areas of Polygons

1 pts
volume_mute

A square has a side length of \(10\text{ cm}\). A triangle has a base of \(20\text{ cm}\) and a height of \(10\text{ cm}\). Compare their areas.

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Identifying Essential Formulas

1 pts

Match each geometric shape to its verified standard interior area formulation.

To complete the line match

  1. Click on an item in the first group
  2. Click on the match in the second group

To delete a match, double click on a line

Shapes

Triangle
Kite
Regular Polygon

Formulas

\(0.5 \times b \times h\)
\(0.5 \times d₁ \times d₂\)
\(0.5 \times a \times P\)
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Explanation

Area of a Scalene Triangle

1 pts

Find the area of a non-right triangle with base \(b = 14\text{ inches}\) and matching altitude height \(h = 9\text{ inches}\).

Answer = (1)

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Key Terminology Matching

1 pts

Type the correct term to finish this sentence:

A flat 2D polygon with four straight edges and exactly one pair of opposing parallel vector lines is designated as a (1).

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Area of an Irregular Hexagon Split

1 pts
volume_mute

An irregular composite region can be cleanly divided into two separate identical parallelograms. Each parallelogram features a base of \(7\text{ cm}\) and a height of \(4\text{ cm}\). Find the total aggregate area.

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Perimeter from regular polygon properties

1 pts

A regular polygon has a total calculated area of \(240\text{ cm}^2\) and an internal apothem length of \(8\text{ cm}\). Calculate its full perimeter boundary path line length.

Answer = (1)

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Explanation

Match shapes with their defintions

1 pts
Figure Name
s s (1)
l w (2)
b h (3)
b h (4)
b₁ b₂ h (5)
Please drag and drop the selected option in the right place or type it instead
Trapezoid
Square
Rectangle
Triangle
Parallelogram
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Explanation

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