Learning Task #1: Directions: Identity the area of the shaded
region of the following composite figures. Write your solutions
below. Choose only 1.
8 m
7 m
2 m
6 m
8 m
5 m

The area of the shaded region ([tex]A_{sr}[/tex]) of these composite figures are calculated by taking the difference between the area of the entire polygon and the area of the unshaded region.

1. RECTANGLE - SQUARE

Area of rectangle: [tex]A=lw[/tex]

Area of square: [tex]A=s^2[/tex]

Solution:

[tex]A_{sr}=[/tex] area of outer shape - area of unshaded inner shape

Area of rectangle (outer):

[tex]A=lw\\A=7\bullet4\\A=28[/tex]

Area of square (unshaded inner):

[tex]A=s^2\\A=2^2\\A=4[/tex]

Area of shaded region

[tex]A_{sr}=28-4\\A_{sr}=24[/tex]

2. SQUARE - TRIANGLE

Area of square: [tex]A=s^2[/tex]

Area of triangle: [tex]A=\frac{1}{2}bh[/tex]

Solution:

[tex]A_{sr}=[/tex] area of outer shape - area of unshaded inner shape

Area of square (outer):

[tex]A=s^2\\A=8^2\\A=64[/tex]

Area of triangle (unshaded inner):

[tex]A=\frac{1}{2} bh\\A=\frac{1}{2} (5)(6)\\A=\frac{1}{2} (30)\\A=15[/tex]

Area of shaded region:

[tex]A_{sr}=64-15\\A_{sr}=49[/tex]

CONCLUSION: You can pick one answer as the simplest.