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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Views #: 245
Questions #: 21
Time: 20 minutes
Pass Score: 80.0%
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Area of a Right Triangle

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Find the area of the right triangle shown below.

b = 11 cma = 15 cm
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Area of a Parallelogram

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Calculate the exact area of the parallelogram provided below.

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

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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

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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

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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

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  2. Click on an item in the second group
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Properties

Perimeter
Total Area

Values

48 units
166.32 sq units

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.

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Properties of Regular Polygons

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Descriptions
×The line segment from the center to a vertex
×The perpendicular distance from center to a side
×Half the product of apothem and perimeter
Apothem
Radius
Area Formula

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

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Area of a Regular Pentagon

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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

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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

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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

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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

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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

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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

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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

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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

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To complete the line match
  1. Click on an item in the first group
  2. Click on an item in the second group
  3. To delete a match, double click on a line

Shapes

Triangle
Kite
Regular Polygon

Formulas

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

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

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Area of a Scalene Triangle

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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

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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

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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

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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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Match shapes with their defintions

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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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