Question

1. calculate the area and perimeter of the following shape:

Explanation:

Step1: Calculate the perimeter

The perimeter of a polygon is the sum of all its side lengths.
$$P = 3 + 2.1+6 + 2.1+3=16.2\ \text{cm}$$

Step2: Calculate the area

We can split the shape into two parts: two congruent triangles and a parallelogram.
The area of a parallelogram is \(A_{para}=b\times h\), where \(b = 6\ \text{cm}\) and \(h = 1.5\ \text{cm}\), so \(A_{para}=6\times1.5 = 9\ \text{cm}^2\)
The base of each triangle is \(3 - 1.5=1.5\ \text{cm}\) and the height of each triangle is \(2.1\ \text{cm}\). The area of a triangle is \(A_{tri}=\frac{1}{2}\times b\times h\). The combined area of the two triangles is \(A_{tri - total}=2\times\frac{1}{2}\times1.5\times2.1 = 3.15\ \text{cm}^2\)
The total area \(A=A_{para}+A_{tri - total}=9 + 3.15=12.15\ \text{cm}^2\)

Answer:

The perimeter is \(16.2\ \text{cm}\) and the area is \(12.15\ \text{cm}^2\)