11.2 -- Area

Links and useful resources

• gr7's Prealgebra Course Outline START HERE<<<
• AoPS Online Textbook
• IXL Grade 7 index
• IXL Grade 8 index
• AoPS Alcumus
• IXL prealgebra practice index
• OpenSTAX Prealgebra-1 textbook

Concept summary and lesson

• Area of a rectangle: $a=w\cdot h$
• Area of a triangle: $a=\frac{1}{2}b\cdot h$
• The "height" of a triangle is the perpendicular distance of the vertex from whichever side you want to use for the base. The formula doesn't care which way is up, it only matters that you have the distance from one of the sides to the vertex opposite to it.

Pay attention to the fact that the area formulas are EQUATIONS! That means you can use the relationship to solve for any of the three missing parts - the area, the width, height, or base (if it's a triangle). You'll need this for several problems.

Finding areas of complex shapes

The trick to finding complex areas is to break them into simple pieces. You can add and subtract areas, so just look for easy shapes and build up a set of them to add together.

Sometimes a shape would be simple if you added more to it, like a rectangle with a corner cut off. In that case, just figure out the area of the rectangle and the area of the missing piece, and subtract.

You can do this as many times as you need in order to find the total area.

Guided practice

• What is the area of each triangle as a fraction of the rectangle it's drawn in?
  

• Ravi and Ranu are expanding their house so that the wall that was 18 feet by 8 feet before will become 25 feet by 8 feet. Ravi still wants a triangle that reaches from one corner to the opposite corner, but he doesn’t want to use any more paint than he used for his triangle on the old wall. Ranu says they’ll just keep the bottom of the triangle the same, and extend the top to the new corner, as shown below. Will this use the same amount of paint as the original?
  

• A median of a triangle is a segment that connects a vertex of the triangle to the midpoint of the opposite side. For example, in the diagram on the right $\overline{AM}$ is a median of $\mathrm{△}ABC$. Show that a median of a triangle divides the triangle into two pieces with equal area.

Homework

• #hw (math) (gr7) 11.2 Area (p. 422) 2025-03-10