Question

Answer the following Question:- (4×1=4)

12. Two sticks each of length 5 cm are crossing each other such that they bisect each other What shape is formed by joining their end points?

13. What is the sum of all the interior angles of a hexagon?

14. What is the length of one of the diagonals of a rectangle of length 10 cm and breadth 24 cm.

15. What is the number of sides of a regular polygon whose interior angle is of 135° each.​

Answer 1

Answer:

12th square

13th 720

14th 26

15th 8

Answer 2

Step-by-step explanation:

Answer 12 :-

Given, two sticks each of length 5cm i.e. equal in length.

If the diagonal of a quadrilateral are equal and bisects each

Other then the quadrilateral is a rectangle. Hence, the shape

Formed by joining given two sticks will be a rectangle.

Answer 13 :-

Sum of interior angles of a Polygon = (n - 2) × 180°

where n = number of sides

where n = number of sidesFor a hexagon, n = 6

Thus, by substituting in the above formula we get

Sum of interior angles of a hexagon = (6 - 2) × 180° = 720°

Thus, the sum of the interior angles of a hexagon is 720°.

Answer 14 :-

Using Pythagoras Theorem,

→ h² = p² + b²

→ h² = 10² + 24²

→ h² = 100 + 576

→ h² = 676

→ h² = 26

Hence, length of it's diagonal is 26 cm.

Answer 15 :-

Given an interior angle of a polygon is 135°.

In mathematics, according to Euclidean Geometry, a polygon that has all sides of the same length and all angles of the same measure is called a regular polygon.

We know that each of all angles of a polygon whose sides and angles are equal is given by (n - 2) × 180°/n, where n is the number of sides.

Interior angle = [(n - 2) × 180] / n.

Applying the interior angle = 135° in the formula, we get

135° = ((n - 2) × 180) / n

⇒ 135 × n = [(n - 2) × 180]

⇒ 135 × n = 180n - 360

⇒ 180n - 135n = 360

⇒ 45n = 360

⇒ n = 360 / 45

⇒ n = 8.

We know that the polygon that has 8 sides is called an octagon.

Hope it helps :)..!!

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