## SAT SUBJECT TEST MATH LEVEL 1

## PLANE GEOMETRY

## CHAPTER 10

Quadrilaterals and Other Polygons

### PERIMETER AND AREA OF QUADRILATERALS

The ** perimeter** (

*P*) of a polygon is the sum of the lengths of all of its sides. The

**(**

*area**A*) of a polygon is the amount of space it encloses (measured in square units). The perimeter and area formulas you need to know for the Math 1 test are given in KEY FACTS I8 and I9.

**Key Fact I8**

**PERIMETERS**

• **For a rectangle: P** =

**2(**+

*w*)• **For a square: P** =

**4**

*s***Key Fact I9**

**AREAS**

• **For a parallelogram: A** =

*bh*• **For a rectangle: A** =

*w*• **For a square: A** =

*s*^{2 }or• **For a trapezoid:**

**TIP**

Here”s a useful alternate formula for the area of a square:

If *d* is the diagonal of a square, then the area of the square is .

**EXAMPLE 3:** What are the perimeter and area of a rhombus whose diagonals are 6 and 8? First draw and label a rhombus.

Since the diagonals bisect each other, *BE* = *ED* = 3 and *AE* = *EC* = 4. Also, since the diagonals of a rhombus are perpendicular, ∠*BEA* is a right angle and *BEA* is a 3-4-5 right triangle. So *AB* = 5 and the perimeter of the rhombus is 4 5 = 20. The easiest way to calculate the area of the rhombus is to recognize that it is the sum of the areas of four 3-4-5 right triangles. Since each triangle has an area of , the area of the rhombus is 4 6 = 24.

**EXAMPLE 4:** In the figure below, the area of parallelogram *ABCD* is 40. What are the areas of rectangle *AFCE*, trapezoid *AFCD*, and triangle *BCF* ?

Since the base of parallelogram *ABCD* is 10 and its area is 40, its height, *AE*, must be 4. Then Δ*AED* must be a 3-4-5 right triangle with *DE* = 3, which implies that *EC* = 7. So the area of rectangle *AFCE* is 7 4 = 28; the area of trapezoid *AFCD* is ; and the area of each small triangle is .