You just found the areas of the 4 triangles. What is the sum of the areas of the 4 triangles? Record that in the equation.
A tilted square on a grid enclosed in another square. The outer square has a side length of 12 units. The 4 triangles formed by intersections of the inner and outer squares are each labeled 18 square units.
area of
outer square	-	sum of the areas
of the 4 triangles	=	area of
inner square
144 units 
2
 	-	
 units 
2
 	=	?


To solve this, let's break it down:

- **Outer square's area**: The side length is 12 units, so the area of the outer square is:
  \[
  \text{Area of outer square} = 12 \times 12 = 144 \text{ square units}
  \]

- **4 triangles' areas**: Each triangle has an area of 18 square units, so the total area of the 4 triangles is:
  \[
  \text{Total area of 4 triangles} = 4 \times 18 = 72 \text{ square units}
  \]

Now, using the given equation:

\[
\text{Area of outer square} - \text{Sum of the areas of the 4 triangles} = \text{Area of inner square}
\]
Substitute the known values:
\[
144 - 72 = \text{Area of inner square}
\]

So, the area of the inner square is:
\[
\text{Area of inner square} = 72 \text{ square units}
\]

The final equation is:
\[
144 - 72 = 72
\]

---

Would you like more details or clarification on any part? Here are 5 related questions to consider:
1. How does the area of a square relate to its side length?
2. How can you calculate the area of a triangle when given the base and height?
3. What geometric properties are important when working with tilted squares and intersections?
4. How do you find the area of a figure when it is enclosed within another shape?
5. How can the concept of symmetry help in solving geometric problems like this?

**Tip**: Remember, the area of a square is calculated as side length squared, and when dealing with intersections and enclosed figures, subtracting areas is key to finding what's left.

You just found the areas of the 4 triangles. What is the sum of the areas of the 4 triangles? Record that in the equation.
A tilted square on a grid enclosed in another square. The outer square has a side length of 12 units. The 4 triangles formed by intersections of the inner and outer squares are each labeled 18 square units.
area of
outer square - sum of the areas
of the 4 triangles = area of
inner square
144 units - ? = ?

Learn how to determine the area of an inner square enclosed within another square by subtracting the areas of four triangles. This problem explores geometric properties, area calculations, and symmetry concepts. Suitable for students in Grades 6-8.

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