The lateral surface area of the shape is 420in²
Lateral surface area is the surface area of a shape without the area of the base.
In the diagram, it has been stated that the base area is shaded
Therefore, the lateral area of the shape is calculated as;
area of rectangle = y × z
y = 7in
z = 24in
area = 24 × 7 = 168in²
area of rectangle = w × y
w = 10in
area = 7 × 10
= 70 in²
area = x × y
x = 26in
26 × 7 = 182in²
lateral area = 168 + 70 + 182
= 420in²