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3 years ago

Find the area of the quadrilateral in the figure.

Mathematics

1 answer:

kirill [66]3 years ago

4 0

<h3>Answer:</h3>

C. 19.64

<h3>Explanation:</h3>

The triangle at upper right is a 3-4-5 right triangle, so has an area that is half the product of the leg lengths:

... upper right area = (1/2)(3 units)(4 units) = 6 units²

The triangle at lower left is an isosceles triangle with base length 5 and side length 6. The altitude to the side of length 5 is a bisector of that side and forms right angles at the point of intersection. Hence we can use the Pythagorean theorem to find the triangle's altitude:

... lower left triangle altitude = √(6² - 2.5²) = √29.75 ≈ 5.45436

Then the area of the lower left triangle is half the product of this altitude and the base length of 5 units:

... lower left area = (1/2)(5.45436 units)(5 units) ≈ 13.6359 units²

The quadrilateral's area is the sum of the areas of these triangles, so is ...

... quadrilateral area = upper right area + lower left area

... = 6 units² + 13.6359 units²

... = 19.6359 units² ≈ 19.64 units²

_____

Confirmed by my geometry program as shown in the attachment.

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Area of a triangle with points at (-9,5), (6,10), and (2,-10)

Ann [662]

First we are going to draw the triangle using the given coordinates.
Next, we are going to use the distance formula to find the sides of our triangle.
Distance formula: $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Distance from point A to point B:
$d_{AB}= \sqrt{[6-(-9)]^2+(10-5)^2}$
$d_{AB}= \sqrt{(6+9)^2+(10-5)^2}$
$d_{AB}= \sqrt{(15)^2+(5)^2}$
$d_{AB}= \sqrt{225+25}$
$d_{AB}= \sqrt{250}$
$d_{AB}=15.81$

Distance from point A to point C:
$d_{AC}= \sqrt{[2-(-9)]^2+(-10-5)^2}$
$d_{AC}= \sqrt{(2+9)^2+(-10-5)^2}$
$d_{AC}= \sqrt{11^2+(-15)^2}$
$d_{AC}= \sqrt{121+225}$
$d_{AC}= \sqrt{346}$
$d_{AC}= 18.60$

Distance from point B from point C
$d_{BC}= \sqrt{(2-6)^2+(-10-10)^2}$
$d_{BC}= \sqrt{(-4)^2+(-20)^2}$
$d_{BC}= \sqrt{16+400}$
$d_{BC}= \sqrt{416}$
$d_{BC}=20.40$

Now, we are going to find the semi-perimeter of our triangle using the semi-perimeter formula:
$s= \frac{AB+AC+BC}{2}$
$s= \frac{15.81+18.60+20.40}{2}$
$s= \frac{54.81}{2}$
$s=27.41$

Finally, to find the area of our triangle, we are going to use Heron's formula:
$A= \sqrt{s(s-AB)(s-AC)(s-BC)}$
$A=\sqrt{27.41(27.41-15.81)(27.41-18.60)(27.41-20.40)}$
$A= \sqrt{27.41(11.6)(8.81)(7.01)}$
$A=140.13$

We can conclude that the perimeter of our triangle is 140.13 square units.

3 0

3 years ago

S = vt + 16t^2, solve for v.

Phoenix [80]

$S=vt+16t^2\ \ \ \ \ | subtract\ 16t^2\\\\
S-16t^2=vt\ \ \ \ \ | divide\ by\ t\\\\
\frac{S-16t^2}{t}=v\\\\\Solution\ is\ v=\frac{S-16t^2}{t}.$

7 0

3 years ago

Maya has 28 apples, 12 oranges, and 8 mangos. She wants to put an equal number of each kind of fruit into baskets so all of the

marysya [2.9K]

12 in each basket.

28÷4= 7
12÷4= 3
8÷4=2
7+3+2= 12

Hope this helps!

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3 years ago

Read 2 more answers

Suppose that start-up companies in the area of biotechnology have probability 0.2 of becoming profitable, and that those in the

Aleks04 [339]

Answer:

<u>The probability that both companies become profitable is 0.03 or 3%.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Probability of biotechnology start-up company of becoming profitable = 0.2

Probability of information technology start-up company of becoming profitable = 0.15

2. Assume the companies function independently What is the probability that both companies become profitable?

We will answer this question, assuming these are independent events, this way:

Probability that both companies become profitable = Probability of biotechnology start-up company of becoming profitable * Probability of information technology start-up company of becoming profitable

Replacing with the values given, we have:

Probability that both companies become profitable = 0.2 * 0.15 = 0.03

<u>The probability that both companies become profitable is 0.03 or 3%.</u>

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3 years ago

The height of a cylinder is twice its radius. A sphere whose radius is 2 inches less than the radius of the cylinder is carved o

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Graphing it out yields the radius of the cylinder is 5 inches.

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3 years ago