Geometry and Area Calculations

The video tutorial covers Lesson 18, focusing on calculating the areas of squares and circles, understanding area ratios, and using algebraic expressions for semicircles and quarter circles. It includes example problems and a practical application involving the design of placemats. The tutorial also explains how to calculate the perimeter and material needed for the placemats and concludes with finding the area of a circle given its circumference.

What is the area of a square with a side length of 12 cm?

• 156 cm²

• 132 cm²

• 120 cm²

• 144 cm²

If a circle has a diameter of 12 cm, what is its radius?

• 9 cm

• 6 cm

• 3 cm

• 12 cm

What is the ratio of the area of half a square to the original square?

• 1:3

• 1:4

• 2:3

• 1:2

How do you express the area of a semicircle algebraically?

• 2πr

• πr²

• 1/2 πr²

• 1/4 πr²

Using π as 22/7, what is the area of a semicircle with a radius of 7 cm?

• 44 cm²

• 154 cm²

• 77 cm²

• 88 cm²

What is the total area of a placemat consisting of a rectangle and two semicircles, if the rectangle is 12x8 inches?

• 132 in²

• 160 in²

• 120 in²

• 146.24 in²

How much fabric is needed for six placemats, each with an area of 146.24 in²?

• 800 in²

• 900 in²

• 732.24 in²

• 877.44 in²

What is the perimeter of a placemat with a rectangle and two semicircles, if the rectangle's length is 12 inches?

• 72 inches

• 60 inches

• 49.12 inches

• 36 inches

If the circumference of a circle is 24π, what is the radius?

• 24

• 18

• 6

• 12

What is the area of a circle with a radius of 12, using π?

• 288π

• 144π

• 72π

• 96π