Take note Theorem 10-3: Area of a Triangle

The area of a triangle is half the product of a base and the corresponding height.

A = 1 2 b h eh equals . 1 half , b h

Problem 3 Finding the Area of a Triangle

Sailing You want to make a triangular sail like the one below. How many square feet of material do you need?

• Step 1 Convert the dimensions of the sail to inches.

  ( 12  ft ⋅ 12  in . 1  ft ) + 2  in . = 146  in .  Use a conversion factor . ( 13  ft ⋅ 12  in . 1  ft ) + 4  in . = 160  in . table with 2 rows and 1 column , row1 column 1 , open 12 , ft dot . fraction 12 , in . , over 1 ft end fraction . close plus 2 in . equals 146 , in , . . cap useaconversionfactor . . , row2 column 1 , open 13 , ft dot . fraction 12 , in . , over 1 ft end fraction . close plus 4 in . equals 160 , in . , end table

• Step 2 Find the area of the triangle.

  A = 1 2 b h     = 1 2 ( 160 ) ( 146 ) Substitute  160  for  b  and  146  for  h .   = 11 , 680 Simplify . table with 3 rows and 3 columns , row1 column 1 , eh , column 2 equals , 1 half , b h , column 3 , row2 column 1 , , column 2 equals , 1 half . open 160 close . open 146 close , column 3 cap substitute . 160 , for , b , and , 146 , for , h . , row3 column 1 , , column 2 equals 11 comma 680 , column 3 cap simplify , . , end table

• Step 3 Convert 11 , 680  in . 2 11 comma 680 , in , . squared  to square feet.

  11 , 680  in . 2 ⋅ 1  ft 12  in . ⋅ 1  ft 12  in . = 81 1 9 ft 2 11 comma 680 , in , . squared , dot . fraction 1 ft , over 12 , in . end fraction . dot . fraction 1 ft , over 12 , in . end fraction . equals 81 , and 1 ninth , ft squared

  You need 81 1 9 ft 2 81 , and 1 ninth , ft squared  of material.

✓ Got It?

3. What is the area of the triangle?

   

Problem 4 Finding the Area of an Irregular Figure

What is the area of the figure below?

Find the area of each part of the figure.

triangle area = 1 2 b h = 1 2 ( 6 ) 8 = 24  in . 2 square area = b h = 6 ( 6 ) = 36  in . 2 area of the figure = 24  in . 2 + 36  in . 2 = 60  in . 2 table with 3 rows and 1 column , row1 column 1 , trianglearea . equals . 1 half , b h . equals , 1 half . open 6 close 8 equals . 24 , in , . squared , row2 column 1 , squarearea . equals b h . equals 6 . open 6 close equals . 36 , in , . squared , row3 column 1 , areaofthefigure . equals . 24 , in , . squared . plus . 36 , in , . squared . equals . 60 , in , . squared , end table

✓ Got It?

4. Reasoning Suppose the base lengths of the square and triangle in the figure above are doubled to 12 in., but the height of each polygon remains the same. How is the area of the figure affected?