Question

answer attempt 1 out of 2 area = units²

Explanation:

Step1: Divide the shape

Divide the given shape into a rectangle and two right - angled triangles. The rectangle EABD has length from \(x=- 2\) to \(x = 6\) (length \(l=8\)) and height from \(y=-2\) to \(y = 1\) (height \(h = 3\)). The two right - angled triangles above the rectangle are congruent.

Step2: Calculate rectangle area

The area formula for a rectangle is \(A_{rect}=l\times h\). Here, \(l = 8\) and \(h=3\), so \(A_{rect}=8\times3 = 24\).

Step3: Calculate triangle area

For each right - angled triangle, the base \(b\) and height \(h_{t}\): The base of each triangle is \(4\) (half of the horizontal distance between the non - vertical sides of the overall shape) and the height is \(6\) (from \(y = 1\) to \(y=7\)). The area formula for a triangle is \(A_{t}=\frac{1}{2}\times b\times h_{t}\). So \(A_{t}=\frac{1}{2}\times4\times6=12\).

Step4: Calculate total area

The total area \(A\) of the shape is the area of the rectangle plus the combined area of the two triangles. Since there are two triangles, \(A = A_{rect}+2A_{t}\). Substitute \(A_{rect}=24\) and \(A_{t}=12\) into the formula: \(A=24 + 2\times12=48\).

Answer:

48