Exploring the Area of Triangles

The video tutorial explains two formulas for calculating the area of a triangle: one using base times height divided by two, and the other using half of the base times height. The instructor demonstrates how these formulas are equivalent and provides examples using whole numbers, decimals, and fractions. The tutorial emphasizes the importance of identifying the base and height that form a right angle and avoiding the use of the slanted side. The video also covers the process of simplifying fractions and converting mixed numbers to improper fractions for calculations.

What are the two ways to write the formula for the area of a triangle?

• Base times height times two and base times height divided by two

• Base plus height divided by two and one-half of the base plus the height

• Base times height divided by two and one-half of the base times the height

• Base times height and base plus height

Why do we divide the area of a rectangle by two to find the area of a triangle?

• To simplify the calculation

• Because a rectangle is made up of two triangles

• To double the area

• Because a rectangle is made up of three triangles

What must the base and height of a triangle form to use the area formula?

• A straight angle

• An acute angle

• A right angle

• An obtuse angle

What is the area of a triangle with a base of 12 and a height of 16?

• 64 square units

• 128 square units

• 192 square units

• 96 square units

When using the first formula for the area of a triangle, what types of side measurements are applicable?

• Both whole numbers and decimals

• Only decimals

• Only whole numbers

• Only fractions

What is the area of a triangle with a base of 7.1 and a height of 8.2?

• 116.44 square meters

• 29.11 square meters

• 58.22 square meters

• 15.55 square meters

How do you convert mixed numbers to improper fractions for multiplication?

• Divide the whole number by the denominator and subtract the numerator

• Subtract the numerator from the whole number and divide by the denominator

• Multiply the whole number by the denominator and add the numerator

• Add the whole number to the numerator and multiply by the denominator

What is the simplified form of the product of 1/2, 21/5, and 5/2?

• 42/5

• 105/10

• 21/4

• 10/21

Why is it important to simplify fractions before multiplying when using the second formula for triangle area?

• To avoid large numbers

• To make division easier

• To find the greatest common factor

• To convert to mixed numbers

For which type of triangle measurements is the formula 'one-half of the base times the height' specifically used?

• Mixed numbers

• Fractions

• Decimals

• Whole numbers