How do I find area of combined rectangles?

Find Areas of Combined Figures Involving Triangles

Sometimes, you will have a figure that uses both triangles and another figure like a parallelogram. We can find the area of the individual parts, add them together and find the total area of the entire figure.

How does this work?

Surveyors use this strategy all the time. When they are figuring out the area of a plot of land, they may divide it up into different figures. Then they find the area of each individual section or figure and add up their answers. The sum is the total area of the figure.

Example 1

Here are a series of triangles that line the center median of a city street. The triangles are overlapping.

Let’s say that that the first triangle has a base of 6 feet and a height of 5 feet. What is the area of the triangle?

A & = / frac{1}{2}bh / / A & = / frac{1}{2} (6) (5) / / A & = / frac{1}{2} (30) / / A & = 15 / square / feet

Let’s say that there are eight triangles in this strip of median. We can take the area of one of the triangles and multiply it by 8.

15 (8) = 120 square feet

This is the area of the median. We were able to use the area of each triangle to find the total area of the median.

Example 2

Here we have a rectangle and a triangle together. If we want to find the total area of the figure, we need to find the area of the rectangle and the area of the triangle and then find the total sum.

Area of the rectangle

A & = lw / / A & = 3 (5) / / A & = 15 / sq. / meters

Area of the triangle

A & = / frac{1}{2}bh / / A & = / frac{1}{2} (1.5) (3) / / A & = 2.25 / sq. / meters

Now we add the two areas together.

Area of rectangle + area of triangle = total area of figure

15 sq. meters + 2.25 sq. meters = 17.25 sq. meters

The total area is 17.25 square meters.

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