Unit 8, Lesson 1
The Areas of Squares
Grade 8
1.1
Warm-up
Which shaded region is larger? Explain your reasoning.
Two quadrilaterals, labeled “A” and “B,” on square grids. Both quadrilaterals are not aligned to the horizontal or vertical gridlines. Quadrilateral “A” is on a grid that has 2 rows of 4 squares. The quadrilateral is drawn starting at the left most vertex. The second vertex is 2 squares to the right and 1 square up from the first vertex. The third vertex is 2 squares to the right and 1 square down from the second vertex. The fourth vertex is 2 squares to the left and 1 square down from the third vertex. The first vertex is 2 squares to the left and 1 square up from the fourth vertex. Quadrilateral “B” is on a grid that has 3 rows of 3 squares. The quadrilateral is drawn starting at the left most vertex. The second vertex is 1 square to the right and 2 squares up from the first vertex. The third vertex is 2 squares to the right and 1 square down from the second vertex. The fourth vertex is 1 square to the left and 2 squares down from the third vertex. The first vertex is 2 squares to the left and 1 square up from the fourth vertex.
1.3
Activity
Find the area of each shaded square (in square units).
Student Lesson Summary
The area of a square with a side length of 12 units is or 144 units2.
Sometimes we want to find the area of a square but we don’t know the side length. For example, how can we find the area of square ?
One way is to enclose it in a square whose side lengths we do know.
The outside square has side lengths of 11 units, so its area is 121 units2. The area of each of the four triangles is , so the area of all four together is units2.
To get the area of the shaded square, we can take the area of the outside square and subtract the areas of the four triangles. So the area of the shaded square is units2.
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