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Area of a rectangle Area of a parallelogram Area of a trapezoid Area of a rhombusInterior angles in polygons
Pythagorean TheoremHere you will learn about the area of a hexagon, including how to find the area of regular hexagons and irregular hexagons.
Students will first learn about the area of a hexagon as part of geometry in high school.
The area of a hexagon is the amount of space inside a hexagon. A hexagon is a katex is not definedD shape also known as a six-sided polygon.
A regular hexagon is a polygon that has katex is not defined sides of equal length and katex is not defined equal interior angles.
The area of a regular hexagon can be found by splitting the shape into congruent triangles, by finding the midpoint of the shape and creating line segments.
You can find the area of one of the triangles and then multiply by the number of sides to find the total area of the regular polygon. This method will work for a regular hexagon, a regular octagon and so on. In the case of a regular hexagon, the triangles will be equilateral triangles.
The area of a regular hexagon can be simplified into the formula,
katex is not definedThe area of the triangle can be found using the formula,
katex is not definedWhere katex is not defined is the base length (or the side of the hexagon) and katex is not defined is the perpendicular height of the triangle. Sometimes these values will need to be calculated.
This means the area of a regular hexagon can also be written as,
katex is not definedUse this quiz to check your grade 4 to 6 students’ understanding of area. 15+ questions with answers covering a range of 4th, 6th and 7th grade area topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 4 to 6 students’ understanding of area. 15+ questions with answers covering a range of 4th, 6th and 7th grade area topics to identify areas of strength and support!
DOWNLOAD FREEAn irregular hexagon may have been formed by different shapes. The area of a hexagon can be calculated by working out the area of each of these shapes and adding them together.
For example,
Area of the irregular hexagon katex is not defined is,
katex is not definedIn order to work out the angles in a regular hexagon, you can use the angle fact that states ‘the sum of angles at a point is katex is not defined
All katex is not defined congruent triangles meet at the center of the hexagon, forming a point, therefore all katex is not defined angles around that center point should sum to katex is not defined
A regular hexagon can be split into katex is not defined congruent equilateral triangles. So, the internal angles of an equilateral triangle are all katex is not defined
The interior angles of these congruent triangles can be used in trigonometry to find the area of each of the equilateral triangles.
Two katex is not defined angles make one of the interior angles of a regular hexagon, so each of the 6 interior angles is katex is not defined
How does this relate to high school math?
In order to find the area of a hexagon:
Find the area of the irregular hexagon katex is not defined
You can split the katex is not defined shape into two rectangles.
2Calculate the area of the parts.
The area of the top rectangle is,
katex is not definedThe area of the bottom rectangle is,
katex is not defined3Calculate the total area of the hexagon.
The total area of the hexagon is found by adding the area of the top and bottom rectangles together.
katex is not defined4Write the answer, including the correct units.
The dimensions of the shape are given in centimeters, so the units of the area will be in square centimeters.
The area of hexagon katex is not defined is katex is not defined
Find the area of the irregular hexagon katex is not defined
Consider the hexagon as a compound shape and split it appropriately.
You can split the katex is not defined shape into two rectangles.
Calculate the area of the parts.
The dimensions of the top rectangle are both in meters.
The area of the top rectangle is,
katex is not defined
To calculate the area of the bottom rectangle, be consistent and use meters. The area of the bottom rectangle is
katex is not defined
Calculate the total area of the hexagon.
The total area of the hexagon is found by adding the area of the two rectangles together.
katex is not defined
Write the answer, including the correct units.
The dimensions of the shape used to calculate the area are meters, so the units of the area will be in square meters.
The area of hexagon katex is not defined is katex is not definedor katex is not defined
Calculate the area of the regular hexagon katex is not defined given that the area of one of the congruent triangles is katex is not defined
Consider the hexagon as a compound shape and split it appropriately.
The hexagon has already been split into six equilateral triangles for us.
Calculate the area of the parts.
The area of one triangle has been given in the question, katex is not defined
Calculate the total area of the hexagon.
The area of the regular hexagon is,
katex is not defined
Write the answer, including the correct units.
The area of hexagon katex is not defined is katex is not defined
Calculate the area of the regular hexagon katex is not defined given that the length of one side of a regular hexagon is katex is not defined Give your answer to katex is not defined decimal place.
Consider the hexagon as a compound shape and split it appropriately.
Here, the regular hexagon katex is not defined has been split into six congruent equilateral triangles.
Calculate the area of the parts.
There are three methods you can use to find the area of an equilateral triangle by forming a right triangle with a right angle. The first two methods to find the height of the triangle are shown below.
The area of one of the equilateral triangles is,
The third method uses the HIGHER trigonometry formula for the area of a triangle.
Calculate the total area of the hexagon.
The area of the regular hexagon is,
katex is not defined
Write the answer, including the correct units.
The dimensions of the shape are given in centimeters, so the units of the area will be in square centimeters.
The area of hexagon katex is not defined is katex is not definedto katex is not defined decimal placekatex is not defined
Calculate the area of the regular hexagon katex is not defined given that the length of the apothem of the regular hexagon is katex is not defined Give your answer to katex is not defined decimal place.
Consider the hexagon as a compound shape and split it appropriately.
Here, the regular hexagon katex is not defined has been split into six congruent equilateral triangles.
Calculate the area of the parts.
You need to work out the base of the triangle.
This can be done using trigonometry with the angles inside the equilateral triangle.
katex is not defined
The base of one of the equilateral triangles is,
katex is not defined
The area of one of the equilateral triangles is,
Calculate the total area of the hexagon.
The area of the regular hexagon is,
Write the answer, including the correct units.
The dimensions of the shape are given in centimeters, so the units of the area will be in square centimeters.
The area of hexagon katex is not defined is katex is not defined katex is not definedto katex is not defined decimal placekatex is not defined
Calculate the area of the regular hexagon katex is not defined given that the length from the center of the hexagon to the vertices is katex is not defined Give your answer in exact form.
Consider the hexagon as a compound shape and split it appropriately.
Here, the regular hexagon katex is not defined is split into six congruent equilateral triangles.
Calculate the area of the parts.
You need to work out the height of the triangle using trigonometry with the angles inside the equilateral triangle. The hypotenuse of the triangle is katex is not defined
katex is not defined
You need to work out the base of the triangle using trigonometry with the angles inside the equilateral triangle. The hypotenuse of the triangle is katex is not defined
katex is not defined
The base of one of the equilateral triangles is,
The area of one of the equilateral triangles is,
The alternative method uses the HIGHER trigonometry formula for the area of a triangle.
Calculate the total area of the hexagon.
The area of the regular hexagon is,
Write the answer, including the correct units.
The dimensions of the shape are given in centimeters, so the units of the area will be in square centimeters.
The area of hexagon katex is not defined is katex is not defined in exact form.
1. Calculate the area of the irregular hexagon katex is not defined Give your answer in square centimeters.
The irregular hexagon katex is not defined can be split into two rectangles.
The area of the top rectangle is
katex is not defined
The area of the bottom rectangle is
katex is not defined
The total area of the irregular hexagon is found by adding the two separate areas together.
katex is not defined
2. Calculate the area of the irregular hexagon katex is not defined Give your answer in square meters.
The irregular hexagon katex is not defined can be split into two rectangles.
The dimensions can also be converted into meters.
katex is not defined
katex is not defined
The area of the top rectangle is
katex is not defined
The area of the bottom rectangle is
katex is not defined
The total area of the irregular hexagon is found by adding the two separate areas together.
katex is not defined
3. Calculate the area of the irregular hexagon katex is not defined given that the area of one of the congruent triangles is katex is not defined
The area formula for a regular hexagon is
katex is not defined
4. Calculate the area of the regular hexagon katex is not defined given that the length of one side of the regular hexagon is katex is not defined
The area of a regular hexagon can be found by splitting it into katex is not defined equilateral triangles and finding the area of one of the triangles and multiplying it by katex is not defined
The area of one of the equilateral triangles is
katex is not defined
The third method uses the HIGHER trigonometry formula for the area of a triangle.
katex is not defined
The area of the regular hexagon is
katex is not defined
5. Calculate the area of the regular hexagon katex is not defined given that the length of the apothem of the regular hexagon is katex is not defined
The area of a regular hexagon can be found by splitting it into katex is not defined equilateral triangles and finding the area of one of the triangles and multiplying it by katex is not defined
The base of the triangle is calculated using trigonometry with the angles inside the equilateral triangle.
katex is not defined
The base of one of the equilateral triangles is
katex is not defined
The area of one of the equilateral triangles is
katex is not defined
The area of the regular hexagon is
katex is not defined
6. Calculate the area of the regular hexagon katex is not defined given that the length from the center of the hexagon to the vertices is katex is not defined
The area of a regular hexagon can be found by splitting it into katex is not defined equilateral triangles and finding the area of one of the triangles and multiplying it by katex is not defined
The height of the triangle can be calculated using trigonometry and the angles in the equilateral triangle.
katex is not defined
The base of the triangle can be calculated using trigonometry and the angles in the equilateral triangle.
katex is not defined
The base of one of the equilateral triangles is
katex is not defined
The area of one of the equilateral triangles is
katex is not defined
The alternative method uses the HIGHER trigonometry formula for the area of a triangle.
katex is not defined
The area of the regular hexagon is
katex is not defined
The formula to find the area of a regular hexagon is:
katex is not defined
To find the perimeter of any hexagon, you add up the length of the sides. To find the perimeter of a regular hexagon, you can simply multiply the length of the hexagon by katex is not defined
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