Question

Find a total surface area of the figure. Figure one is a rectangular shape with a base of 7 mm height, the 4 mm and a length of 12 mm on top of this rectangle tangle there is another rectangular shape with a height of 5 mm base of 5 mm

Answer 1

To find the total surface area of the figure described, we need to calculate the surface area of both rectangular shapes separately and then add them together.

### Shape 1: Bottom Rectangle
This rectangle has:
- Base (width) = 4 mm
- Height = 7 mm
- Length = 12 mm

#### Surface Area of Shape 1:
The surface area of a rectangle is calculated as:

\[
\text{Surface Area} = 2 \times (\text{Width} \times \text{Height} + \text{Height} \times \text{Length} + \text{Length} \times \text{Width})
\]

Substituting in the values for Shape 1:

\[
= 2 \times (4 \, \text{mm} \times 7 \, \text{mm} + 7 \, \text{mm} \times 12 \, \text{mm} + 12 \, \text{mm} \times 4 \, \text{mm})
\]
\[
= 2 \times (28 + 84 + 48)
\]
\[
= 2 \times 160 = 320 \, \text{mm}^2
\]

### Shape 2: Top Rectangle
This rectangle has:
- Base (width) = 5 mm
- Height = 5 mm
- Length = 12 mm (assuming it has the same length as the bottom rectangle)

#### Surface Area of Shape 2:
Using the same formula for calculating the surface area:

\[
= 2 \times (5 \, \text{mm} \times 5 \, \text{mm} + 5 \, \text{mm} \times 12 \, \text{mm} + 12 \, \text{mm} \times 5 \, \text{mm})
\]
\[
= 2 \times (25 + 60 + 60)
\]
\[
= 2 \times 145 = 290 \, \text{mm}^2
\]

### Total Surface Area
Now, add the surface areas of both shapes:

\[
\text{Total Surface Area} = \text{Surface Area of Shape 1} + \text{Surface Area of Shape 2}
\]
\[
= 320 \, \text{mm}^2 + 290 \, \text{mm}^2 = 610 \, \text{mm}^2
\]

Thus, the total surface area of the figure is **610 mm²**.