Question

A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 1.2 feet.

What is the surface area of the actual ramp, including the underside?

Enter your answer as a decimal in the box.

Answer 1

Answer:

16.8

Step-by-step explanation:

Answer 2

The scale factor is a ratio. The surface area of the real ramp is 16.80 ft².

What is the scale factor?

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

As we know that the height of the real ramp is 1.2 feet, while the height of the drawing is 6 cm, therefore, the scale factor can be written as,

$\rm Scale\ factor = \dfrac{\text{Area of Image}}{\text{Area of pre-image}}=\dfrac{1.2 \ feet}{6\ cm} = 0.2$

Now, the area of the pre-image can be written as,

$\rm \text{Area of pre-image} = 2triangles+ 2 rectangle + 1 rectangle\ at\ base$

                             $= 2(0.5 \times 6 \times 16) + 2(10 \times 9) + (16 \times 9)\\\\= 2(48)+2(90)+144\\\\= 96 + 180 + 144\\\\ = 420\ cm^2$

Further, the area of the actual ramp can be written as,

${\text{Area of pre-image}} \times \rm Scale\ factor = \text{Area of Image}\\\\ \text{Area of Image}= 420 \times (0.2)^2 \\\\ \text{Area of Image}= 16.8\ ft^2$

Hence, the surface area of the real ramp is 16.80 ft².

Learn more about Scale Factor:

https://brainly.com/question/22644306