An isosceles trapezoid with bases 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior
1 answer:
The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.
<h3>Height of the trapezoid</h3>The height of the trapezoid is calculated as follows;
From the image, the sum of h1 and h2 is the height of the trapezoid.
Each of the height will be calculated using Pythagoras theorem as follows;
- half of b1 = 12/2 = 6
- half of b2 = 16/2 = 8
h1² = r² - (b1/2)²
h1² = 10² - 6²
h1² = 64
h1 = √64
h1 = 8
h2² = r² - (b1/2)²
h2² = 10² - 8²
h2² = 36
h2 = √36
h2 = 6
Total height = 8 + 6 = 14
<h3>Area of the trapezoid</h3>A = ¹/₂(b₁ + b₂)H
A = ¹/₂(12 + 16) x 14
A = 196 sq units.
Learn more about area of trapezoid here: brainly.com/question/1463152
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There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question. I do the first two ways.
Step One
Graph the two equations.
The graph is below.
Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D
Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6
Step 4
Solve
6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x Pull the 2 terms on the left over to the right.
6x - 5x = -x^2
x = - x^2
x^2 + x = -x^2 + x^2
x^2 + x = 0 Factor
x(x + 1) = 0
That means that
x = 0
or
x + 1 = 0
x = - 1
Step 3
Find the ys
y = 6x + 6
if x = -1
y = 6(-1) + 6
y = -6 + 6
y = 0
One of the answers is
(-1,0) <<<<<<<< Answer
Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6
The other point is (0,6) answer <<<<<<<
D <<<<<< Total answer
There are 3 ways you could solve this
1. You could graph it.
2. You could equate the line to the quadratic
3. You could just put the x value of the points into both equations until you get the same y value. It sometimes is the only way to solve a multiple choice math question. I do the first two ways.
Step One
Graph the two equations.
The graph is below.
Step 2
From the graph determine the answers.
There are two points where the graphs coincide
Check out D
Step 3
Equate the two equations. The y values must be the same.
6x + 6 = -x^2 + 5x + 6
Step 4
Solve
6x + 6 = - x^2 + 5x + 6 The 6s cancel which is very handy.
6x = -x^2 + 5x Pull the 2 terms on the left over to the right.
6x - 5x = -x^2
x = - x^2
x^2 + x = -x^2 + x^2
x^2 + x = 0 Factor
x(x + 1) = 0
That means that
x = 0
or
x + 1 = 0
x = - 1
Step 3
Find the ys
y = 6x + 6
if x = -1
y = 6(-1) + 6
y = -6 + 6
y = 0
One of the answers is
(-1,0) <<<<<<<< Answer
Now for the other one
y = 6x + 6
x = 0
y = 6(0) + 6
y = 6
The other point is (0,6) answer <<<<<<<
D <<<<<< Total answer