Explanation

The sum of the internal angles of a polygon can be found using the formula:

(n-2) × 180°

where n is the number of sides.

For a regular octagon (8 sides):

(8-2) × 180° = 6 × 180° = 1080°

Since it's a regular octagon, all internal angles are equal. To find the measure of each internal angle, divide the total sum by the number of angles:

1080° ÷ 8 = 135°

Explanation

Given:

Perimeter = 294 m

Length = 85 m

Let's denote the width as W. The formula for the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

294 = 2(85 + W)

147 = 85 + W

W = 62 m

Now, to find the area:

Area = Length * Width

= 85 * 62

= 5270 m²

Explanation

Altitude is the shortest perpendicular distance from the base to the opposite vertex in a geometric figure (such as a triangle).

Median, on the other hand, is a line segment joining a vertex to the midpoint of the opposite side.

Explanation

Equilateral Triangle Three equal angles, always 60

all sides are of equal length (equilateral), and all  angles are right angles. 

A triangle that has no equal sides and no equal angles is known as a Scalene Triangle

while 

if two sides of a triangle are of equal length, then it is called. Isosceles triangle

Explanation

Length = x³ - x + 2

= (2)³ - 2 + 2

= 8 - 2 + 2

= 8

Width = x + x²

= 2 + (2)²

= 2 + 4

= 6

Area = Length * Width

= 8 * 6

= 48

Explanation

Pythagoras is considered the founder of the basic laws of geometry.

His work, particularly the Pythagorean theorem.

This laid foundational principles for the study of geometry.

Explanation

Given:

Side length of square = 31 meters

Perimeter formula: P = 4 × side

P = 4 × 31

P = 124 meters

Explanation

Given a right-angled triangle with a base angle of 45°, it's an isosceles right triangle, meaning the base and perpendicular are equal.

Base length = 3 dm

Perpendicular length = 3 dm

Explanation

Explanation

The area of a parallelogram is given by the formula: Area = base × altitude.

Substituting the given values: 36 = base × 4, hence base = 36 / 4 = 9 meters.