Area of Rectangles with Fractional Side Lengths

Rectangles and Triangles with Fractional Lengths

By Molly Olson

Open Ended

What do you notice? What do you wonder?

If a rectangle has side lengths a units and b units, the area is a*b square units. For example, if we have a rectangle with 1/2-inch side lengths, its area is 1/4 square inches.​

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Area of a rectangle​

Multiple Choice

Kiran says “A square with side lengths of $$\frac{1}{3}$$   inch has an area of $$\frac{1}{3}$$  square inches.” Do you agree?

• Yes

• No

Multiple Choice

Find the area of a rectangle that is $$1\ \frac{1}{2}$$   inches by $$2\ \frac{1}{2}$$   inches.

• $$\frac{15}{4}\ in^2$$  

• $$2\ \frac{1}{4}in^2$$  

• $$\frac{6}{10}in^2$$  

• $$4\ \ in^2$$  

Multiple Choice

Carolina planted seeds in a box that measured 7/8 meter long and  3/5 meter wide. What is the area of the garden box?

• 10/13 square meter
• 24/35 square meter
• 21/40 square meter
• 34/50 square meter

Multiple Choice

 A rectangle has a width of 2 1/4  inches and a height of 5/8 inch. Which of the following equations describes the area of the rectangle?

• 2/4 x 5/8= 10/32 square inch
• 9/4 x 5/8 = 14/12 square inches
• 7/4 x 5/8= 35/32 square inches
• 9/4 x 5/8 = 45/32 square inches

Multiple Choice

You can use the formula is
A = 1/2 b⋅h to find the area of every triangle.

• True
• False

• Any side can be a base.

• A segment that represents a height must be drawn at a right angle to the base, but can be drawn in more than one place. The length of this perpendicular segment is the distance between the base and the vertex opposite it.

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​Area of triangles

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Multiple Choice

Find the area of Triangle A in square centimeters.

• 9 sq. cm

• $$8\ \frac{1}{4\ }sq\ cm$$  

• $$10\ \frac{1}{8}sq\ cm$$  

• $$\frac{81}{2}\ sq\ cm$$  

Multiple Choice

The area of Triangle B is 8 square units. Find the length of b.

• 2

• $$\frac{8}{3}$$  

• 3

• 6

Draw

The area of Triangle C is 54/5

square units. What is the length of h? Show your reasoning.

Multiple Choice

What multiplication equation can we write to help us find the height of a triangle that has a base of $$\frac{5}{4}$$   cm and an area of 10 sq cm?

• $$10\times\frac{4}{5}\times2=16\ cm$$  

• $$\frac{5}{4}\times10=\frac{50}{4}cm$$  

• $$\frac{5}{4}\times10\times\frac{1}{2}=\frac{25}{4}\ cm$$  

• $$10\times\frac{4}{5}\times\frac{1}{2}=4\ cm$$