# Area Problems with Fractional Side Lengths

Videos, examples, solutions, and lessons to help grade 5 students learn how to solve real world problems involving area of figures with fractional side lengths using visual models and/or equations.

### New York State Common Core Math Module 3, Grade 5, Lesson 15

Lesson 15 Concept Development

Problem 1
The length of a flowerbed is 4 times as long as its width. If the width is 3/8 meter, what is the area?

Problem 2
Mrs. Johnson grows herbs in square plots. Her basil plot measures 5/8 yd on each side.
a. Find the total area of the basil plot.
b. Mrs. Johnson puts a fence around the basil. If the fence is 2 ft from the edge of the garden on each side, what is the perimeter of the fence?
c. What is the total area that the fence encloses?

Problem 3
Janet bought 5 yards of fabric 2 1/2 feet wide to make curtains. She used 1/3 of the fabric to make a long set of curtains and the rest to make 4 short sets.
a. Find the area of the fabric she used for the long set of curtains.
b. Find the area of the fabric she used for each of the short sets.

Problem 4
Some wire is used to make rectangles: A, B, and C. Rectangle B’s dimensions are 3/5 cm larger than Rectangle A’s dimensions, and Rectangle C’s dimensions are 3/5 cm larger than Rectangle B’s dimensions. Rectangle A is 2 cm by 3 1/2 cm.
a. What is the total area of all three rectangles?
b. If a 40-cm coil of wire was used to form the rectangles, how much wire is left?

Lesson 15 Problem Set and Homework

1. The length of a flowerbed is 4 times as long as its width. If the width is 3/8 meter, what is the area?

(Homework) 1. The width of a picnic table is 3 times its length. If the length is 5/6 yd long, what is the area in square feet?

2. A painting company will paint this wall. The homeowner gives them the following dimensions:
Window A is 6 1/4 ft x 5 3/4 ft.
Window B is 3 1/8 ft x 4 ft
Window C is 9 1/2 ft square
Door D is 8 ft x 4 ft
What is the area of the painted part of the wall?

1. Some wire is used to make 3 rectangles: A, B, and C. Rectangle B’s dimensions are 3/5 cm larger than Rectangle A’s dimensions, and Rectangle C’s dimensions are 3/5 cm larger than Rectangle B’s dimensions. Rectangle A is 2 cm by 3 1/5 cm.
a. What is the total area of all three rectangles?
b. If a 40-cm coil of wire was used to form the rectangles, how much wire is left?

(Homework) 3. A decorative wooden piece is made up of four rectangles as shown to the right. The smallest rectangle measures 4 1/2 by 7 3/4 inches. If 2 1/4 inches is added to each dimension as the rectangles get larger, what is the total area of the entire piece?

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