Formulas for Area and Perimeter

This video tutorial explains how to calculate the perimeter of various geometric shapes, including equilateral triangles, squares, and circles, using their areas. It begins with an introduction to the concept and then provides detailed methods for each shape. For equilateral triangles, the video demonstrates using the area formula to find side length and then the perimeter. For squares, it simplifies the process by using the square root of the area. Finally, it covers finding the circumference of a circle from its area using a specific formula. The tutorial concludes with a quiz to test understanding.

Which shapes are discussed in the video for finding the perimeter from the area?

• Equilateral triangles, squares, and circles

• Rectangles, pentagons, and hexagons

• Cubes, spheres, and cylinders

• Trapezoids, rhombuses, and ellipses

What is the formula for the area of an equilateral triangle with side length 's'?

• Area = s^2 * sqrt(2) / 4

• Area = s^2 / 2

• Area = s^2 * 3 / 4

• Area = s^2 * sqrt(3) / 4

If an equilateral triangle has an area of 1251.141 cm², what is its perimeter?

• 102 cm

• 51 cm

• 34 cm

• 68 cm

What is the formula to find the perimeter of a square from its area?

• Perimeter = 4 * sqrt(area)

• Perimeter = 2 * area

• Perimeter = area / 4

• Perimeter = 4 * area

If a square has an area of 225 square units, what is its perimeter?

• 45 units

• 30 units

• 90 units

• 60 units

What is the formula to find the circumference of a circle from its area?

• Circumference = area / pi

• Circumference = 2 * pi * sqrt(area)

• Circumference = pi * area

• Circumference = 2 * sqrt(pi * area)

If a circle has an area of 1,000 km², what is its circumference?

• 314 km

• 56 km

• 112.0714 km

• 200 km

What value of pi is used in the calculation for the circumference of a circle?

• 3.0

• 3.14159

• 3.14

• 3.2

Which of the following is NOT a step in finding the circumference of a circle from its area?

• Multiplying the area by pi

• Dividing the area by 2

• Taking the square root of the product

• Multiplying the result by 2

What is the final step in calculating the circumference of a circle from its area?

• Divide the square root by 2

• Multiply the square root by 2

• Add pi to the square root

• Subtract pi from the square root