Question

the outside square efgh has side lengths of 11 units, so its area is 121 units². the area of each of the four triangles is ½·8·3 = 12, so the area of all four together is 4·12 = 48 units². to get the area of the shaded square, we can take the area of the outside square and subtract the areas of the 4 triangles. so the area of the shaded square abcd is 121 − 48 = 73 or 73 units².

Explanation:

Step1: Identify outside square area

The outside square EFGH has side length 11, so area is \(11\times11 = 121\) square units.

Step2: Calculate one triangle's area

Each triangle has base 8 and height 3. Area of a triangle is \(\frac{1}{2}\times base\times height=\frac{1}{2}\times8\times3 = 12\) square units.

Step3: Find total area of four triangles

There are 4 triangles, so total area is \(4\times12 = 48\) square units.

Step4: Subtract triangle area from outside square

Shaded square area = Outside square area - Total triangle area = \(121 - 48 = 73\) square units.

Answer:

The area of the shaded square \(ABCD\) is \(\boldsymbol{73}\) square units.