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3 years ago

What is the total area of the shape below

Mathematics

2 answers:

brilliants [131]3 years ago

6 0

Answer:

480 ft

Step-by-step explanation:

Nadya [2.5K]3 years ago

5 0

Answer:

480ft²

explanation:

first of all, find the area of the rectangle as it is the easiest.
So, do A = L x W.

A = 24 x 15
= 360ft²

Then find the area of half of the triangle.
So, do A = 1/2 x b x h

The length of the base of the full triangle (aka top of the rectangle) is 24ft so since we are finding the area of half of the triangle all you have to do it half 24 (12). (also 1/2 is the same as 0.5)

So the equation for that would be
A = 1/2 x b x h
= 1/2 x 12 x 10
= 1/2 x 120
= 60

So now, to find the area of the whole triangle, times 60 by 2 (as both of the halves are the same) which gives you 120.

Finally, to find the area of the WHOLE shape, do 360ft² + 120ft² which gives you 480ft².

Hope this helps :)

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1 year ago

A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

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Step-by-step explanation:

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