Geometry Concepts and Problem Solving

The video tutorial covers various geometric shapes and their properties, including equilateral triangles, rectangles, rhombuses, parallelograms, spheres, cones, trapezoids, and rectangular prisms. It explains how to calculate areas, volumes, and solve equations using algebraic techniques. The tutorial also applies trigonometry to real-world scenarios, providing a comprehensive overview of these mathematical concepts.

What is the area of an equilateral triangle with a side length of 10?

• 25√3

• 75√3

• 50√3

• 100√3

In a rectangle, if one diagonal is 15, what is the length of the other diagonal?

• 25

• 20

• 15

• 10

If one angle in a rhombus is 50 degrees, what is the measure of the opposite angle?

• 60 degrees

• 70 degrees

• 50 degrees

• 40 degrees

Which quadrilateral has diagonals that are always congruent?

• Rectangle

• Rhombus

• Trapezoid

• Parallelogram

What is the area of a parallelogram with a base of 10 and a height of 2√3?

• 40√3

• 30√3

• 20√3

• 10√3

Given the volume of a sphere is 972π, what is its radius?

• 6

• 9

• 7

• 8

What is the volume of a cone with a radius of 8 and height of 6?

• 384π

• 256π

• 128π

• 512π

If the angle of elevation is 3 degrees, what is the horizontal distance to the lighthouse?

• 100/tan(30)

• 100/cos(3)

• 100/sin(3)

• 100/tan(3)

Solve the system: 17x + 6y = 193 and 13x + 7y = 191. What is x?

• 3

• 6

• 4

• 5

If AC is 49 and AB is 45, what is the length of BC?

• 7

• 6

• 5

• 4