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 heigh
1 answer:
The surface area of the actual ramp including the underside is 16.8 ft²
The height of the actual ramp = 1.2 feet
The height of the model = 6 cm
<h3>What is the surface area of a right triangular prism?</h3>A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm
Actual base = 16 cm × 0.2 ft/cm = 3.2 ft
convert the units
9 cm = 9 cm × 0.2 ft/cm = 1.8 ft
10 cm = 10 cm × 0.2 ft/cm = 2 ft
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)
= 16.8 ft²
Hence, the surface area of the actual ramp including the underside is 16.8 ft²
Learn more about the area here:
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Answer:
70/9
Step-by-step explanation:
We have the quadratic:
So, let’s find the roots of the quadratic. We will set the expression equal to 0:
Testing for factors, we can see that our quadratic isn’t factorable.
So, we can use the Quadratic Formula. The quadratic formula is given by:
In this case:
Therefore, by substitution:
Evaluate:
Simplify the square root:
Hence:
Reduce:
So, our roots are:
We want to find the sum of the <em>squares</em> of our two roots. So, let’s square each term:
Square. For the numerator, we can use the perfect square trinomial patten where:
Therefore:
Simplify:
Similarly, for the second root, we will have:
So:
Simplify:
Therefore, our sum will be:
Therefore, our final answer is 70/9.