Question

b) 12 cm 4 cm 9 cm area:

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 12\space cm\) and \(w=4\space cm\), so \(A_{rectangle}=12\times4 = 48\space cm^{2}\).

Step2: Calculate the area of the white triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). Here, \(b = 9\space cm\) and \(h = 4\space cm\), so \(A_{triangle}=\frac{1}{2}\times9\times4= 18\space cm^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{rectangle}-A_{triangle}\). Substitute the values: \(A=48 - 18=30\space cm^{2}\).

Step4: Calculate the perimeter of the figure

The perimeter of the figure: sum of all outer - sides. The sides are \(12\space cm\), \(4\space cm\), \((12 - 9)=3\space cm\), and the two non - base sides of the triangle. Using the Pythagorean theorem for the non - base sides of the triangle: \(a=\sqrt{4^{2}+3^{2}} = 5\space cm\) (for each non - base side of the triangle). The perimeter \(P=12 + 4+3 + 5+5=29\space cm\).

Answer:

Area: \(30\space cm^{2}\), Perimeter: \(29\space cm\)