Geometry Concepts and Problem Solving

The video tutorial covers the application of special right triangles, specifically 45-45-90 triangles, in solving various geometry problems. It includes practical examples such as calculating the distance between playing cards, determining the size of a tablecloth, finding the area of a square garden, and calculating segment lengths in a circle. The tutorial also explains how to calculate the perimeter of shapes and the area of a trapezoid, emphasizing the use of radical forms and rounding techniques.

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 6.3 cm?

• 8.9 cm

• 9.0 cm

• 6.3 cm

• 12.6 cm

If a tablecloth has a diagonal of 46 inches, what should be the side length of the square tablecloth?

• 34 inches

• 35 inches

• 32 inches

• 33 inches

Given a square garden with a diagonal of 18 meters, what is the length of each side?

• 12.7 meters

• 13.0 meters

• 12.5 meters

• 13.5 meters

What is the area of a square garden with a diagonal of 18 meters?

• 180.0 square meters

• 161.3 square meters

• 150.0 square meters

• 170.0 square meters

If the circumference of a circle is 20π cm, what is the radius?

• 15 cm

• 10 cm

• 20 cm

• 5 cm

In a circle with a radius of 10 cm, what is the length of the diagonal in a 45-45-90 triangle formed inside?

• 10√2 cm

• 10 cm

• 20 cm

• 15 cm

What is the perimeter of a shape with sides 18√2, 43, 18, and 25?

• 110 units

• 120 units

• 100 units

• 111.5 units

How do you calculate the area of a trapezoid?

• 1/2 × base × height

• 1/2(base1 + base2) × height

• base × height

• base1 + base2 + height

If a trapezoid has bases of 26 and 14, and a height of 12, what is its area?

• 260 square units

• 200 square units

• 220 square units

• 240 square units

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 10 cm?

• 10√2 cm

• 15 cm

• 10 cm

• 20 cm