Find the area of the quadrilateral in the figure.
1 answer:
<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
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Confirmed by my geometry program as shown in the attachment.
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Parallelograms have equal and parallel opposite sides
<em>The coordinates of the 4th point is (-2,3)</em>
Let the parallelogram be ABCD, such that:
A and B have the same y-coordinates, while their x-coordinates are additive inverse
This means that:
The y-coordinates of point C and point D will be the same, while their x-coordinates will be additive inverse.
<u>For point C</u>
We have:
<u>For point D</u>
The coordinates would be:
Hence, the coordinates of D is (-2,3)
Read more about parallelograms at:
Answer:
The values of x are x = -2 and x= 1.
Step-by-step explanation:
The given equation -x²+4 = x+2 can be written in the form of two functions as
y = -x²+4 which is a function representing parabola and
y = x+2 which is a straight line.
Now we will solve the given equation to find their points of intersection on graph. Their points of intersections will be the answer.
-x²+4 = x+2
-x²+4-x = x+2-x
-x²-x+4 = 2
-x²-x+4-2 = 2-2
-x²-x+2 = 0
Or x²+x-2=0
Now we will factorize the equation.
x²+2x-x-2=0
x(x+2)-1(x+2) = 0
(x+2)(x-1) = 0
x+2 = 0 ⇒x = -2
x-1 = 0 ⇒x = 1
For x = 1, y will be 3
and for x = -2, y will be 0
Now we can see the graph for the given coordinates (-2,0) and (1,3).
