1. Example 1 Finding a Combined Area ARCHITECTURE Two methods can be used to find the total area of the two rectangular rooms. A replica of the Parthenon, a temple in ancient Greece, was built in Nashville, Tennessee, in 1897. The diagram below shows the approximate dimensions of two adjacent rooms inside the replica. You can find the total area of the rooms in two ways, as shown.

2. Example 1 Finding a Combined Area 2772 = +6174 8946 square feet = Area 63(44) = +63(98) METHOD 1Find the area of each room, and then add the two areas. METHOD 2Find the total length, and then multiply by the common width. Area 63(44 = +98) 63(142) =

3. Example 1 Finding a Combined Area 8946 square feet = ANSWER The total area of the two rooms is 8946 square feet.

4. Example 2 Using the Distributive Property a. x–5+10( ) = x–5+ ) 10( () Distributive property = x–5+–50 )( Multiply. = x–5 – 50 Simplify. b. 3 – 201 +–5 ) ( [] = – 320 () Distributive property 1 () 3+–5 () 3 = – 360 Multiply. +–15 () = – 72 Add from left to right.

5. Use the distributive property to find the area of the rectangle. 1. 2. ANSWER 340 ft 2 ANSWER 168 m 2 Guided Practice for Examples 1 and 2

6. Guided Practice for Examples 1 and 2 Evaluate the expression or write an equivalent expression. ANSWER –34 ANSWER 68 3. –2+5 )( 12 4. –4––7 )( 10 5. 2–w ) ( 8 6. –8+z ) ( 25 ANSWER 2–w16 ANSWER –8–z200