Unit 2, Lesson 14
Find the Area of a Figure with Unknown Side Lengths
Grade 3
Warm-up
Notice and Wonder: Mystery Sides
What do you notice? What do you wonder?
6-sided shape. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 4 cm. Left side rises ? cm, then goes left ? cm, and goes up 2 cm. Top side length, 10 cm. Right side length, 9 cm.
Activity 1
The Mystery Side
Tyler says that this figure’s unknown side length is 5 meters because it looks longer than the sides that are 4 meters long.
Do you agree or disagree? Be prepared to explain your reasoning.
Activity 2
Practice with Mystery Sides
Find the area of each figure. Explain or show your reasoning.
8-sided shape. Straight sides. All side lengths meet at right angles. Bottom, question mark ft. Right side rises 4 ft then goes right 2 ft, then up 2 ft. Top side length, 7 ft. Left side goes down 2 ft, then right 3 ft, then down question mark ft.
Student Section Summary
We found the area of a figure that can be decomposed, or broken apart, into rectangles. We added the areas of the rectangles to find the area of the entire figure.
We also found unknown side lengths of figures by using what we know about opposite sides of rectangles.
6-sided shape. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 4 cm. Left side rises ? cm, then goes left ? cm, and goes up 2 cm. Top side length, 10 cm. Right side length, 9 cm.
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