Triangle Area and Properties

This video tutorial explains how to find the area of an isosceles triangle using two methods: the basic formula involving base and height, and Heron's formula. It begins with an introduction to the properties of isosceles triangles and the necessary components for calculating area. The video demonstrates how to find the height using the Pythagorean theorem and then calculates the area. It also covers Heron's formula as an alternative method for verifying the area when all side lengths are known. The tutorial concludes with a practice problem to reinforce the concepts.

What is a key characteristic of an isosceles triangle?

• It has no equal sides.

• All angles are equal.

• Two sides are of equal length.

• All sides are of different lengths.

Which formula is used to calculate the area of a triangle when the base and height are known?

• Base times height

• Base plus height

• Base divided by height

• One half base times height

What theorem is used to find the height of an isosceles triangle when the base and one side are known?

• Heron's theorem

• Sine rule

• Pythagorean theorem

• Triangle inequality theorem

If the base of a right triangle is 8 and the hypotenuse is 17, what is the height?

• 10

• 9

• 12

• 15

What is the first step in using Heron's formula to find the area of a triangle?

• Use the Pythagorean theorem

• Multiply the base and height

• Find the semi-perimeter

• Calculate the height

What is the semi-perimeter of a triangle with sides 16, 17, and 17?

• 32

• 34

• 50

• 25

In the practice problem, what is the base of the isosceles triangle?

• 14

• 7

• 25

• 24

What is the height of the isosceles triangle in the practice problem using the base-height method?

• 24

• 12

• 15

• 18

What is the area of the triangle calculated using the base-height method in the practice problem?

• 140

• 150

• 168

• 120

Using Heron's formula, what is the area of the triangle in the practice problem?

• 140

• 168

• 150

• 120