Answer Verified
Hint: First we should draw the diagram of a 7-sided polygon. Now we will find the name of a 7-sided polygon. We know that an 8-sided polygon is said to be an octagon. Now we should assume the number of sides of an 8-sided polygon. Let us assume this equation as equation (1). We know that the sum of interior angles of a n-sided polygon is equal to \[(n-2)180\]. Let us assume this equation as equation (2). Now we should substitute equation (1) in equation (2). This will give us the sum of
internal angles of a regular octagon.Complete step-by-step answer: This diagram represents a heptagon. From this diagram, we can say that the regular polygon of 7 sides is called a heptagon. In the question, we were given that to find the sum of interior angles of a regular octagon. We know that an 8-sided polygon is said to be an octagon. It is clear for us that the above diagram represents an octagon. \[\Rightarrow n=8...(1)\] Let us assume that the sum of interior angles of regular n-sided polygon is equal to A, then \[\Rightarrow A=(n-2)180....(2)\] So, from equation (1) and equation (2), we will find the sum of interior angles of an octagon. \[\begin{align} & \Rightarrow A=(8-2)(180) \\ & \Rightarrow A=1080 \\ \end{align}\]. So, it is clear that the sum of interior angles of an octagon is equal to 1080. Hence, we can say that option (B) is correct. Note: Students generally read this type of question in an incorrect manner. They may read that it was given to find the sum of interior angles of a regular heptagon. A heptagon is a two-dimensional shape with 7 sides and 7 angles. It belongs to the class of polygons in two-dimensional geometry. Polygons are closed shapes made up of straight lines and no curves. “Hepta” means seven and “gonia” means
angle in the Greek language. By combining these two words, the word “heptagon” is formed, meaning a shape with seven angles. In Latin, this polygon is known as septagon, where “septa” means seven and “gon” means angle. Properties of Heptagon $⦣1 + ⦣2+ ⦣3+ ⦣4+
⦣5+ ⦣6+ ⦣7 = 900°$ Types of Heptagon There are two types of heptagons based on their shapes. They can be seen below. Properties of a Regular Heptagon For example, look at the given image of the coin and the arrow. Both the objects have 7 sides and are closed, and therefore, heptagonal in shape. However, the coin is in the shape of a regular heptagon, with all sides and angles equal to each other, and the arrow is an irregular heptagon with sides of different lengths and different angles. So, don’t be confused when you see such an image, because this is as much a heptagon as the image below! Concave and Convex Heptagon There are two other types of heptagons as can be seen below.
Perimeter of a Heptagon The perimeter of a shape means the total length of its boundary. For a polygon, the perimeter is given by given by Let’s say we have a regular heptagon with each side measuring “a” unit, Perimeter $= a + a + a + a + a + a + a = 7 \times$ a units. Real-life Examples In real life, though we may not always notice them, there are multiple examples of heptagons. Some of them are mentioned below.
Solved Examples1. Find out the perimeter of a regular heptagon with a side of 15 cm. Solution: We know that the perimeter of a regular heptagon of side length a is given by, Perimeter $= 7 \times$ a, For the given heptagon, a $= 15$ cm, Therefore, perimeter $= 7 \times 15 = 105$ cm 2. Find the perimeter of an irregular heptagon with sides measuring 7 cm, 8 cm, 9 cm, 10 cm, 11 cm, 12 cm, and 13 cm. Solution: Perimeter is given by, Perimeter $=$ Sum of all sides Therefore, the perimeter of given irregular heptagon $= 7 \text{cm} + 8 \text{cm} + 9 \text{cm} + 10 \text{cm} + 11 \text{cm} + 12 \text{cm} + 13 \text{cm} = 70 \text{cm}$ 3. What is the side of a regular heptagon with a perimeter of 224 cm? Solution: We know that the perimeter of a regular heptagon of side length a is given by, Perimeter $= 7 \times$ a, It is given that, Perimeter $= 224$ cm Therefore, Perimeter $= 7 \times \text{a} = 224$ cm a $= 2247$ a $= 32 $cm Practice Problems
5 6 7 9 Correct answer is: 7 128.57 degrees 152.57 degrees 108 degrees 90 degrees Correct answer is: 128.57 degrees 49 cm 148 cm 144 cm 84 cm Correct answer is: 84 cm 132 cm 168 cm 240 cm 112 cm Correct answer is: 112 cm 22 cm 29 cm 15 cm 30 cm Correct answer is: 22 cm Frequently Asked QuestionsHow many angles are there in a heptagon? There are 7 angles in a heptagon. What is the difference between regular and irregular heptagon? All the sides of a regular heptagon are equal in length, and all angles are equal in degree, while those of an irregular heptagon may vary. Also, there are no parallel sides in a regular heptagon, while there may be some in an irregular heptagon. How many diagonals can you draw in a convex heptagon? There are 14 diagonals in a convex heptagon, all of which lie inside the heptagon. What is the area of a heptagon? Area of a heptagon is the space occupied by the heptagon. If the length of the side of a regular heptagon is s, its area can be calculated using the simplified formula $3.634 \times s^2$. |