Find the area of parallelogram if side AB = 10 cm,BC=15 cm,Diagonal =20 cm.
15/2 √279
Steve, what was that formula?
I don't know how Steve got those numbers, it comes out to appr 125.3
I made a sketch.
I extended BC to E so the DE is an altitude and triangle DCE is right-angled.
I let CE = x and DE = h
x^2 + h^2 = 100, and
(x+15)^2 + h^2 = 400
subtract them
(x+5)^2 - x^2 = 300
30x + 225 = 300
x = 75/30 = 5/2
then h^2 = 100 - 25/4 = 375/4
h = 5√15/2
area = base x height
= 15(5√15)/2 = 75√15/2 cm^2 or appr 145.2 cm^2
or
look at triangle BCD, it is half the area of the parallogram
by the cosine law:
400 = 225 + 100 - 2(10(15)cosC
cosC = (225+100-400)/300 = -1/4
then sinC = √ (1 - 1/16) = √15/4
area of triangle BCD
= (1/2)(10)(15)sinC
= 75√15/4
area of ||gram = 2(75√15/4) = 75√15/2
same as above
Hmmm. Better go with Reiny. I thought my answer was a bit odd.
To find the area of a parallelogram, you need to know either the lengths of the sides or the length of the base and the corresponding height. In the given information, we have the lengths of the sides AB and BC, but we don't have the height. However, we do have the length of one of the diagonals.
To find the area of the parallelogram, we can use the formula:
Area = base × height
The base of the parallelogram can be represented by side AB or side BC. Since both sides have different lengths, we need to find the height first.
To find the height, we can use the diagonal and the formula of the height of a parallelogram in terms of the diagonals. The formula is:
Height = (2 × Area) / (length of diagonal)
In this case, we have the length of the diagonal as 20 cm. However, we don't know the area yet.
To find the area, we can use the formula:
Area = (base × height) / 2
Now let's calculate the height:
Height = (2 × Area) / (length of diagonal)
To find the area, substitute the values we have:
Area = (base × height) / 2
Now we can substitute the known values:
Area = (10 cm × height) / 2
But we still need to find the height, which we can do using the formula:
Height = (2 × Area) / (length of diagonal)
Substituting the known values:
Height = (2 × Area) / (20 cm)
Simplifying:
Height = Area / 10 cm
Now, substitute the height back into the original area formula:
Area = (10 cm × (Area / 10 cm)) / 2
Simplifying:
Area = (Area / 2)
To eliminate the fraction, we can multiply both sides by 2:
2 × Area = Area
Now, divide both sides by Area:
2 = 1
This means that the area can be any value. However, this is not possible, and it suggests that there might be an error or missing information in the given data. Please double-check the values provided or provide additional information.