Question

6 cm 12 cm 6 cm 8 cm 10 cm 6 cm [not drawn to scale] What is the surface area of the three-dimensional figure?

a288 cm
b312 cm
c336 cm
D 368 cm​

Answer 1

C. 336 cm²

Explanation:

Area formulas:

• Area of a right triangle: a × b ÷ 2
• Area of rectangle: length × width

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In this figure, there is a rectangle with a width of 12 and a height of 6.

`12 *6 = 72`; the area of the rectangle is 72 cm².

There are two right triangles with legs of 6 and 8.

`6 * 8 / 2 = 24.`

There are two right triangles so..

`24 * 2 = 48.`

The area of a single triangle is 24 cm²; the area of the triangles combined is 48 cm.

There is a rectangle in the middle with a width of 8 and a height of 12.

`12 * 8 = 96.`

The area of the rectangle is 96 cm².

Lastly, there is a rectangle with a width of 10 and a height of 12.

`12 *10 = 120.`

The area of the rectangle is 120 cm².

Now, add the areas of every shape to find your answer.

`72 + 24 + 24 + 96 + 120 = 336.`

Therefore, the surface area of this three-dimensional figure is 336 cm².