Calculating Areas and Percentages

The video tutorial explains how to solve a practice SAT math question involving calculating the percentage of an unshaded area in a diagram. The problem is approached using two methods: a geometric method involving the calculation of triangle areas and a trigonometric method using properties of right triangles. Both methods lead to the conclusion that 25% of the diagram is unshaded. The tutorial provides a step-by-step explanation of each method, ensuring a clear understanding of the problem-solving process.

What is the size of the smaller square in the problem?

• 2 inches by 2 inches

• 1 inch by 1 inch

• 3 inches by 3 inches

• 4 inches by 4 inches

How do you calculate the total area of the larger square?

• Multiply 1 by 1

• Multiply 2 by 2

• Multiply 3 by 3

• Multiply 4 by 4

What is the base of the unshaded triangle in the first method?

• 2 units

• 3 units

• 1 unit

• 1/2 unit

How many unshaded triangles are there in the diagram?

• 2

• 3

• 4

• 5

What is the percentage of the diagram that is unshaded using the first method?

• 10%

• 25%

• 15%

• 20%

In the second method, what type of triangle is used to find the unshaded area?

• 30-60-90 triangle

• 45-45-90 triangle

• Equilateral triangle

• Scalene triangle

What is the length of each leg of the right triangle in the second method?

• 1/2 unit

• 2 units

• 3 units

• 1 unit

What is the hypotenuse of the right triangle in the second method?

• Square root of 2

• Square root of 3

• 1 unit

• 2 units

What is the area of the larger white square in the second method?

• 1

• 2

• Square root of 2

• 4

What is the final percentage of the unshaded area using the second method?

• 25%

• 20%

• 15%

• 10%