Question

activity 1 - area of composite figures
question #5 - determine the area of the shaded region in each
figure.
what is the area of the square?
what is the area of one of the four small triangles?
what is the area of the four small unshaded triangles
together?
what is the area of one of the four larger unshaded triangles?
what is the area of all four of the larger unshaded triangles
what is the area of the shaded region?
2
prior attempt

Explanation:

Step1: Calculate the area of the square

The side length of the square is \(3 + 6+3=12\) cm. Using the formula for the area of a square \(A = s^2\), we have \(A=(3 + 6+3)^2=12^2 = 144\) sq.cm.

Step2: Calculate the area of one small triangle

The base and height of one small triangle: base \(b = 3\) cm, height \(h=3\) cm. Using the formula for the area of a triangle \(A=\frac{1}{2}bh\), we get \(A=\frac{1}{2}\times3\times3 = 4.5\) sq.cm.

Step3: Calculate the area of four small triangles

Since there are four small triangles, and the area of one small triangle is \(4.5\) sq.cm, the area of four small triangles is \(4\times4.5=18\) sq.cm.

Step4: Calculate the area of one larger unshaded triangle

The base of one larger unshaded triangle \(b = 3 + 6+3-(3 + 3)=6\) cm, height \(h = 6\) cm. Using the formula \(A=\frac{1}{2}bh\), we have \(A=\frac{1}{2}\times6\times6= 18\) sq.cm.

Step5: Calculate the area of four larger unshaded triangles

Since there are four larger unshaded triangles, the area is \(4\times18 = 72\) sq.cm.

Step6: Calculate the area of the shaded region

The area of the shaded region is the area of the square minus the area of four small triangles and four larger unshaded triangles. So \(A=144-(18 + 72)=54\) sq.cm.

Answer:

What is the area of the square? \(144\) sq.cm
What is the area of one of the four small triangles? \(4.5\) sq.cm
What is the area of the four small unshaded triangles together? \(18\) sq.cm
What is the area of one of the four larger unshaded triangles? \(18\) sq.cm
What is the area of all four of the larger unshaded triangles? \(72\) sq.cm
What is the area of the shaded region? \(54\) sq.cm