Page 141 - Math Course 1 (Book 2)

Geometric Area: Composite Figures

Find the Area of a Composite First, separate the f gure into regions. Draw an
Figure to Solve a Problem
auxiliary line perpendicular to QR from M (we will

Example call this point S), an auxiliary line from N to the
x-axis (we will call this point K), and an auxiliary
line from P to the Origin, O.
A rectangular rose garden is centered in a border
of lawn. Find the area of the lawn around the
garden in square feet. This divides the f gure into triangle MRS, triangle

NKM, trapezoid POKN and trapezoid PQSO.

Now, f nd the area of each of the f gures.

Find the difference between y-coordinates to f nd
the lengths of the bases of the triangles and the
The length of the entire lawn is 25 + 100 + 25 or lengths of the bases of the trapezoids.
150 feet. The width of the entire lawn is 25 + 20 +
25 or 70 feet. The length of the rose garden is 100
feet and the width is 20 feet. Find the difference between x-coordinates to f nd
the heights of the triangles and trapezoids.
area of composite f gure =
area of entire lawn– area of rose garden
area of MNPQR = area of △MRS + area of △NKM
= b h – b h Area formulas + area of trapezoid POKN + area of trapezoid PQSO
1 1 2 2
Area formulas
= 150(70)–100(20) Substitution

= 10,500–2000 Simplify. = ½bh + ½bh + ½h(b + b ) + ½h(b + b )
1
2
2
1
= 8500 Simplify. Substitution
The area of the lawn around = ½(2)(9)+ ½(1)(4)+ ½(3)(5 + 4)+ ½h(5)(5 + 3)
Answer the garden is 8500 square
feet. Simplify.
= 44.5

Coordinate Plane The area of polygon MNPQR
Answer is 44.5 square units.
Example

Find the area of polygon MNPQR.

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