Lesson 12-3: Solve Problems Involving Area and Surface Area

Property

To express a mixed-unit measurement like height in a single unit, convert the smaller unit into a fraction or decimal of the larger unit. For example, to convert 6 ft 3 in. to feet:

Examples

• Convert a run time of 8 minutes and 30 seconds to minutes: $8 \text{ min } 30 \text{ sec} = 8\frac{30}{60} \text{ min} = 8\frac{1}{2} \text{ min} = 8.5 \text{ min}$
• Convert a movie length of 2 hours and 15 minutes to hours: $2 \text{ hr } 15 \text{ min} = 2\frac{15}{60} \text{ hr} = 2\frac{1}{4} \text{ hr} = 2.25 \text{ hr}$
• Convert a room width of 10 ft 6 in. to feet: $10 \text{ ft } 6 \text{ in.} = 10\frac{6}{12} \text{ ft} = 10.5 \text{ ft}$

Explanation

Stop juggling two different units! To simplify a measurement like 'feet and inches,' turn the smaller part into a fraction of the bigger one. Then, just add it to the whole number part for a clean, single-unit answer. It makes calculations so much easier when everything speaks the same language.

Property

Decomposition means breaking an irregular figure into smaller, non-overlapping shapes that you already know.
Total Area = Area of Shape 1 + Area of Shape 2 + ...

Examples

• L-Shape: An L-shaped room can be split into two rectangles. If one rectangle measures 12 by 4 units (Area = 48) and the other is 2 by 6 units (Area = 12), the total area is 48 + 12 = 60 square units.
• House Shape: A shape looks like a house. It is formed by a rectangle (8 by 4 units, Area = 32) with a triangle on top (base 8, height 3, Area = 12). The total area is 32 + 12 = 44 square units.

Explanation

Think of this method like building with LEGOs! You break down a strangely shaped room or garden into simple blocks like rectangles and triangles. Calculate the area of each individual block, and then simply add them all together to get the total area.