### All SSAT Middle Level Math Resources

## Example Questions

### Example Question #162 : Geometry

Refer to the above figures. The square at left has area 160. Give the area of the rectangle at right.

**Possible Answers:**

**Correct answer:**

The area of the square, whose sides have length , is the square of this sidelength, which is . The area of the rectangle is the product of the lengths of its sides; this is

The square and the rectangle have the same area, so the correct response is 160.

### Example Question #163 : Geometry

Figure NOT drawn to scale.

Figure 1 and Figure 2 have the same area. The shaded portion of Figure 1 has area 64. What is the area of the shaded portion of Figure 2?

**Possible Answers:**

**Correct answer:**

Figure 1 is a rectangle divided into 24 squares of equal size; 3 of the squares are shaded, which means that of Figure 1 is shaded.

Figure 2 is a circle divided into 8 sectors of equal size; 1 is shaded, which means that of Figure 2 is shaded.

Since the two figures are of the same area, the two shaded portions, each of which have an area that is the same fraction of this common area, must themselves have the same area. Since the shaded portion of Figure 1 has area 64, so does the shaded portion of Figure 2.

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