Given:
LM
||
KN
,
KL
||
NM
,
LP = h1 = 5 cm, MQ = h2 = 6 cm,
PKLMN = 42 cm
Find: Area of KLMN.
Given that in a quadrilatral KLMN,
LM ∥ KN , KL ∥ NM , h1=5, h2=6,
and the perimeter of KLMN is 42.
Since opposite sides are given to be parallel, the quad has to be a parallelogram.
Parallelogram has sides l and w (say)
Then area of parallelogram = base x height
=l(5)=w(6) ... i
Perimeter =2l+2w=42 ... ii
Multiply equation II by 3
6l+6w=42
Substitute for w from i
6l+5l=42
l=42/11
Area = 42/11(5) = 630/11 square units
Where are P and Q in relation to K and N?
they are the opposite sides
To find the area of quadrilateral KLMN, we can use the formula for the area of a trapezoid.
The formula for the area of a trapezoid is:
Area = ((a + b) / 2) * h
where 'a' and 'b' are the lengths of the parallel sides (bases) and 'h' is the height.
In this case, we are given the lengths of two sides (LP and MQ) and the height (h1 and h2).
Let's assign the given lengths and heights to the corresponding sides of the trapezoid:
LP = a
MQ = b
h1 = h
h2 = h
We can see that sides LP and MQ are parallel to each other, so they are the two bases of the trapezoid.
Now, we can substitute these values into the formula:
Area = ((a + b) / 2) * h
Substituting, we get:
Area = ((LP + MQ) / 2) * h
Area = ((5 + 6) / 2) * h
Area = (11 / 2) * h
Now, we need to find the value of h.
To find the height (h) of the trapezoid, we can use the Pythagorean theorem.
Looking at the given figure, we can see that the two triangles (LMK and KMN) are both right triangles.
We can find the height by finding the length of the segment that is perpendicular to the base LM and intersects the base KN.
Using the Pythagorean theorem, we can find the height as follows:
h^2 = LM^2 - LP^2
h^2 = KN^2 - MQ^2
Plugging in the given values, we get:
h^2 = 1^2 - 5^2
h^2 = 1 - 25
h^2 = -24
Since we cannot take the square root of a negative number, we can conclude that there is an error in the given information or figure. Please check the given values and try again.