Lesson 2 Module 5 Gr. 6 EngageNY

5/11 Lesson 2 Mod. 5 Gr 6

Formula for the Area of Right Triangles

What are some properties of a right triangle?

• Three-sided polygon

• one interior angle must measure exactly  $90\degree$  

Can you predict the formula for finding the area of the triangle?

Multiple Choice

Given the length of 3 units and the height of 2 units; what would be the area of the rectangle?

• $2\cdot3=6\$ sq. units

• 2 + 3 =5 sq. units

Open Ended

If the formula for finding the area of a rectangle is Length x width, what would be the formula for finding the area of a right-triangle.

Rectangles can be divided into two right triangles.

• The formula for a rectangle is length x height.

• So the formula for the area of a right triangle is 

•  $A=\ \frac{b\cdot h}{2}$  also written as  $A=\frac{1}{2}\ b\cdot h$  

• (multiply by 1/2 is the same as divide by 2)

Multiple Choice

To find the area of the right triangle that has a length of 3 units and a width of 3 units you would. Multiply 3 x 3 and divide by 2.

• True

• False

How do we know this is correct?

• because we know that right triangle is 1/2 of the rectangle we can use the formula for the rectangle (length x width) and divide it by 2 ( or multiply by 1/2).

How do we determine which side of the triangle is the base and which side is height?

• because the sides form a right triangle are perpendicular, they form the right angle, so it doesn't matter which of these two sides is labeled the base and which is labeled the height.

• the commutative property of multiplication allows us to calculate the formula in any order.

Calculate the area of the right triangle

Start with identifying the two numbers to be multiplied. Length is 15, height is 8. Multiply 15 x 8 = 120 Then divide by 2 (or multiply by 1/2).
The area is $\ \frac{15\cdot8}{2}\ =60$  

Multiple Select

What is the formula to find the area of this right triangle?

• $\frac{6\cdot8}{10}$

• $\frac{8\cdot6}{2}$

• $\frac{6\cdot8\cdot10}{2}$

• $\frac{6\cdot8}{2}$

Multiple Choice

Which is the correct formula and answer for the area of this right triangle?

• $\frac{11\cdot2}{17}$

• $\frac{11\cdot17}{2}$

Open Ended

How are the area formulas of rectangles and right triangles related?

Multiple Choice

Which is the correct formula and answer for the area of this right triangle?

•  $\frac{8\cdot5}{2}\ =20\ m^2$ 

•  $\frac{8\cdot2}{5}\ =3.2\ m^2$ 

Closing

• How are the formulas of rectangles and right triangles related?

• When the two sides that form the right angle are the same length in both a rectangle and a right triangle, the area of the right triangle is exactly half of the area of the rectangle.

• Therefore, the area of the rectangle divided by 2 (or multiplied by half) is equal to the area formula of the right triangle.