What is the area of this parallelogram? 10.35 cm² 12.5 cm² 20.25 cm² 30.6 cm² Parallelogram A B C D is composed of a square and
two triangles. The square has a length and height of 4.5 centimeters each. There are two identical triangles. Each triangle has a base of 2.3 centimeters and a height of 4.5 centimeters.
2 answers:
Answer:
30.6 cm²
Step-by-step explanation:
Dividing the parallelogram into 2 geometry shapes:
Square
2 Right angle triangles
Area of a square, As = length^2
= 4.5^2
= 20.25 cm^2
Area of a right angle triangle, At = 1/2 × base × height
= 1/2 × 2.3 × 4.5
= 5.175 cm^2
Sinve there are 2 right angle triangle,
At = 2 × 5.175
= 10.35 cm^2
Total area of the parallelogram, Ap = area of the square + area of the 2 right angle triangle
= 10.35 + 20.25
= 30.6 cm^2
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Please consider the attached file.
We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.
We will use Pythagoras theorem to solve for KJ as:
Now we will take positive square root on both sides:
Therefore, the length of line segment KJ is and option D is the correct choice.
Step-by-step explanation:
Let's represent the two integers with the variables and
.
From the problem statement, we can create the following two equations:
With the first equation, we can subtract from both sides to isolate the
variable to the left-hand side:
Now that we have a value for , we can plug it into the second equation and solve for
:
Now, let's move everything to one side of the equation:
Factoring this quadratic will give us two values for :
Since we now know , we can plug this back into either of the original equations to get a value for
, which will be
.
So the two numbers that sum to and have a product of
are
.