Question

problems 7 - 8: determine the area of each shaded figure.
8.
7.
reflection

Explanation:

Step1: Count full - squares

Count the number of full - unit squares within the shaded region.

Step2: Combine partial squares

Combine the partial squares to form full - unit squares. For example, two half - squares make one full square.

Step3: Sum up the squares

Add the number of full - squares from Step1 and Step2 to get the area.

For problem 7:

• There are 6 full squares and 4 half - squares. The 4 half - squares are equivalent to 2 full squares. So the area is $6 + 2=8$ square units.

For problem 8:

• The outer square has side length 6 units, so its area is $A_{outer}=6\times6 = 36$ square units.
• The inner non - shaded square can be divided into smaller right - triangles. The non - shaded region can be seen as composed of 4 right - triangles. Each right - triangle has base and height equal to 3 units. The area of one right - triangle is $A_{triangle}=\frac{1}{2}\times3\times3=\frac{9}{2}$ square units. The area of the 4 right - triangles (non - shaded region) is $4\times\frac{9}{2}=18$ square units.
• The area of the shaded region is $A = 36-18 = 18$ square units.

Answer:

Problem 7: 8 square units
Problem 8: 18 square units