Exploring Area and Perimeter of Polygons with Distance Formula

What is the primary purpose of the distance formula in geometry?

• To calculate the slope of a line

• To find the distance between two points on a coordinate plane

• To determine the angle between two lines

• To calculate the radius of a circle

How do you calculate the distance between two points that are aligned horizontally or vertically?

• By using the Pythagorean theorem

• By counting the units between the points

• By applying the midpoint formula

• By using trigonometric ratios

What theorem is the distance formula derived from?

• Euler's theorem

• Fermat's Last Theorem

• The Pythagorean theorem

• The theorem of similar triangles

What is the distance between two points with coordinates (-5, -4) and (-6, 4)?

• The square root of 82

• 8 units

• The square root of 65

• 65 units

How do you find the perimeter of a polygon in a coordinate plane?

• By using the Pythagorean theorem

• By adding the lengths of all its sides

• By multiplying the base with the height

• By calculating the area and dividing by the number of sides

What is the length of the side AB in a triangle if the coordinates of A and B are given and calculated using the distance formula?

• The square root of 100 units

• 10 units

• 100 units

• 20 units

What is the perimeter of a triangle with sides measuring 10 units, 10 units, and the square root of 40 units?

• 26.3 units

• The square root of 100 units

• 20 units plus the square root of 40

• 30 units

How do you calculate the area of a triangle in a coordinate plane?

• Base plus height divided by 2

• Base times height divided by 2

• Half the product of its diagonals

• Base times height

If the base of a triangle is 10 units and its height is 6 units, what is its area?

• 20 units squared

• 60 units squared

• 16 units squared

• 30 units squared

What is the significance of the perpendicular height in calculating the area of a triangle?

• It helps in identifying the type of triangle

• It determines the slope of the triangle

• It is used to calculate the perimeter

• It is essential for finding the triangle's area