Question

1. Use the figure below to answer the questions.

Answer 1

Answer:

A = 144 cm^2

Step-by-step explanation:

a.

The 3D shape shown in the image is a prism, known because it has two parallel faces called bases (the front and back triangles) and the other faces being parallelograms.

b.

To compute the total surface area, we must add the area of the five faces of the shape.

For the bases:

$\displaystyle A_b=2\cdot \frac{bh}{2}=bh$

For the upper face

$A_u=z.w$

Where z is the hypotenuse of the triangle and w is the depth of the prism.

For the face-down surface

$A_d=b.w$

For the right face

$A_r=h.w$

The total area is

$A=bh+zw+bw+hw=bh+w(z+b+h)$

c.

$A=4\times 3+11(5+3+4)=12+132=144$

$A=144\ cm^2$