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Find Areas - Composite figures

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Lesson Plans and Worksheets for Grade 3
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Videos, examples, solutions, and lessons to help Grade 3 students learn how to find areas by decomposing into rectangles or completing composite figures to form rectangles.

Common Core Standards: 3.MD.6, 3.MD.7a, 3.MD.7b, 3.MD.7c, 3.MD.7d, 3.MD.5

New York State Common Core Math Module 4, Grade 3, Lesson 13 and Lesson 14

Lesson 13 Application Problem

Anil finds the area of a 5 inch by 17 inch rectangle by breaking it into 2 smaller rectangles. Show one way that he could have solved the problem. What is the area of the rectangle?

Note: This problem reinforces the strategy of breaking a larger shape apart into 2 smaller shapes to find the total area.

Lesson 13 Concept Development

Problem 1: Add using the break apart strategy to find area of a composite shape.
Problem 2: Subtract to find area of a composite shape.
Problem 3: Subtract to find area of a composite shape with missing side lengths. Lesson 13 Problem Set

1. Each of the following figures is made up of 2 rectangles. Find the total area of each figure.
Figure 1: Area of A + Area of B: 18 + _________ = _________ sq units
Figure 2: Area of C + Area of D: ________ + _________ = __________ sq units
Figure 3: Area of E + Area of F: ________ + _________ = __________ sq units
Figure 4: Area of G + Area of H: ________ + _________ = __________ sq units

2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded region.
Area of the shaded region: ______ ֠______ = ______ sq cm

3. The figure shows a small rectangle cut out of a big rectangle.
a. Label the missing measurements.
b. Area of the big rectangle: ______ נ______ = ______ sq cm
c. Area of the small rectangle: ______ נ______ = ______ sq cm
d. Find the area of the shaded region.



Lesson 13 Homework

1. Each of the following figures is made up of 2 rectangles. Find the total area of each figure.
Figure 1: Area of A + Area of B: _____ + ______ = ______ sq units
Figure 2: Area of C + Area of D: _____ + ______ = _______ sq units
Figure 3: Area of E + Area of F: _____ + ______ = _______ sq units
Figure 4: Area of G + Area of H: _____ + ______ = _______ sq units

2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded region.

3. The figure shows a small rectangle cut out of a big rectangle. Lesson 14 Application Problem

a. Break apart the shaded figure into 2 rectangles. Then add to find the area of the shaded figure below.

b. Subtract the area of the unshaded rectangle from the area of the large rectangle to check your answer in Part (a).

Note: This problem reviews G3–M4–Lesson 13’s concept of finding area of composite shapes. Students may choose to break apart their rectangles in different ways for Part (a).

Lesson 14 Concept Development

Problem 1: Choose an appropriate method for finding the area of a composite shape.
Problem 2: Solve a word problem involving area of non- rectangular shapes. Lesson 14 Homework

1. Find the area of each of the following figures. All figures are made up of rectangles.

2. The figure below shows a small rectangle cut out of a big rectangle.
a. Label the side lengths of the unshaded region.
b. Find the area of the shaded region.

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