Geometry – Triangles and Trapezoids

 All Triangles are related to rectangles or parallelograms : Each rectangle or parallelogram is made up of two triangles! You can draw a diagonal line in any rectangle or parallelogram.

 The area formula for a rectangle or a parallelogram is: A = bh  Each triangle is ½ of a rectangle or a parallelogram.  There are two triangles in these shapes!

 The area formula for a triangle is  It can also be written as

The height is outside the triangle The height is inside the triangle The height is a side of the triangle Determine which measurement is the height :

 Many times shapes (including triangles ) are rotated or hidden in pictures.  Find height and base in these examples: The height is 6.4 m and the base is 12.1 m. The height is 9 cm and the base is 10 cm. The height is 4 yards and the base is 7 yards.

 Select the correct area formula:

 Write the area formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the area formula substituting the values that you know.  Solve one step at a time rewriting after each step. A = ½ bh A = ½ × 15.6 × A = ½ × A = square meters

 Trapezoids have four sides and only one set is parallel.  All Trapezoids are also related to rectangles or parallelograms : If you take them apart and reconstruct them, they will take up the same amount of space as their associated rectangle or parallelogram.

 The bases are the parallel sides. They may or may not be actually located on the top or bottom.  The height will be similar to finding the height of a triangle. It will ALWAYS be perpendicular to the bases. base 1 base 2 The height is outside the parallelogram. Fig. 2 or 4 presented with the longer base on the top. The height is inside the parallelogram. Figures 2 and 4. The height is a side of the parallelogram. Figures 1 and 3.

 The area formula for a rectangle or a parallelogram is: A = bh  Since trapezoids have two bases, you must find the average of the sum of them.  Basically, you will be finding the average (or mean) of the two bases.

 The area formula for a trapezoid is  It can also be written as  Part of one base is on the top, the rest of it is on the bottom. So, you must add them together! The division by two completes the average of the bases. Base 1

 Determine which measurement is the height : The height is inside the trapezoid The height is a side of the trapezoid The bases are the parallel lines. The shape has been rotated! The trapezoid has been used to describe a part of Florida!

 Select the correct area formula:

 Write the area formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the area formula substituting the values that you know.  Solve one step at a time rewriting after each step. A = ½ h(b 1 +b 2 ) A = ½ × 51( ) A = ½ × 51(64) A = 51 × 32 A = 1,632 square miles Look to find half of an even number to make the math easier!

 The shapes have two dimensions.  When you multiply one measurement by another measurement you end up with square units.  For Example: Square Feet ft 2 Square Inches in 2 Square Centimeters cm 2

1.The triangle on the top. 2.The trapezoid beneath the triangle.

1.A = ½ bh A = ½ 11 × 5 A = ½ × 55 A= 27.5 sq. feet 2.A = ½ h(b 1 + b 2 ) A = ½ × 10( ) A = ½ × 10(19.5) A = 5 × 19.5 A = 97.5 sq. feet Remember: Look to find half of an even number to make the math easier!

 Follow the same set of steps as before!  Write the area formula exactly as it appears on the FCAT Reference Sheet.  Rewrite the area formula substituting the values that you know.  Solve one step at a time rewriting after each step.

 Solve the following problem:  Find the base of a triangle if its height is 14 inches and its area is 245 square inches. A = ½ bh 245 = ½ × b × =7 × b Divide by 7 on both sides to undo the multiplication! 35 in. = b

 Solve the following problem:  Find the missing base of a trapezoid with an area of 1,440 square centimeters, a height of 32 centimeters, and one base equal to 40 centimeters. A = ½ h(b 1 + b 2 ) 1,440= ½ × 32(40 + b 2 ) 1,440= 16(40 + b 2 ) Divide by 16 on both sides to undo the multiplication! 90 = 40 + b 2 Subtract 40 on both sides to undo the addition! 50 cm = b 2

 Remember to use the area formulas on the FCAT Reference Sheet: