In trapezoid CDEF, angle D = angle E=90degrees. Angle C =60 degrees, EF=4.5cm, and DE=3.5cm. What is the perimeter of the trapezoid to the nearest mm?
To find the perimeter of the trapezoid, we need to sum up the lengths of all its sides.
In the given information, we can see that angle D and angle E are right angles (90 degrees), and angle C is 60 degrees. This tells us that the trapezoid has a right angle at each end of the longer base.
Let's label the trapezoid as shown below:
C _______ D
/ \
/ \
F ___________ E
Since angle C is 60 degrees, we know that triangle CDE is an equilateral triangle. This means that all sides of this triangle are equal in length.
Given that DE = 3.5 cm, this means that CD = DE = 3.5 cm.
Now, let's find the length of EF.
Since angle D and angle E are also right angles, we can treat triangle DEF as a right-angled triangle.
Using the Pythagorean theorem, we have:
EF^2 = DE^2 + DF^2
(4.5)^2 = (3.5)^2 + DF^2
20.25 = 12.25 + DF^2
DF^2 = 20.25 - 12.25
DF^2 = 8
DF = sqrt(8)
DF = 2.83 cm (rounded to two decimal places)
Now that we have the lengths of all sides, we can calculate the perimeter:
Perimeter = CD + EF + DE + DF
Perimeter = 3.5 + 4.5 + 3.5 + 2.83
Perimeter ≈ 14.33 cm
Therefore, the perimeter of the trapezoid to the nearest mm is approximately 14.33 cm.
To find the perimeter of trapezoid CDEF, we need to add up the lengths of all four sides.
Given:
Angle D = 90 degrees
Angle E = 90 degrees
Angle C = 60 degrees
EF = 4.5 cm
DE = 3.5 cm
To find the lengths of the remaining sides, we can use trigonometry.
1. Find the length of DF:
In triangle DEF, we can use the Pythagorean theorem since angle D is 90 degrees.
DF^2 = DE^2 + EF^2
DF^2 = 3.5^2 + 4.5^2
DF^2 = 12.25 + 20.25
DF^2 = 32.5
DF ≈ √32.5
DF ≈ 5.7 cm (rounded to one decimal place)
2. Find the length of CF:
In triangle CDF, we can use the sine rule.
sin(C) / CF = sin(D) / DF
sin(60) / CF = sin(90) / 5.7
CF = (sin(60) * 5.7) / sin(90)
CF ≈ (0.866 * 5.7) / 1
CF ≈ 4.9 cm (rounded to one decimal place)
3. Find the length of CD:
CD = CF + DE
CD = 4.9 + 3.5
CD ≈ 8.4 cm (rounded to one decimal place)
4. Find the length of CE:
CE = CF + EF
CE = 4.9 + 4.5
CE ≈ 9.4 cm (rounded to one decimal place)
Now, we can calculate the perimeter by adding up all four sides:
Perimeter = CD + DE + EF + CE
Perimeter ≈ 8.4 + 3.5 + 4.5 + 9.4
Perimeter ≈ 25.8 cm (rounded to one decimal place)
Therefore, the perimeter of trapezoid CDEF is approximately 25.8 cm.
Drop a perpendicular from G on CD to F.
Now you have a rectangle GDEF with sides 3.5 and 4.5
Also, triangle CGF where
CG = 3.5/√3
CF = 7.0/√3
Now the perimeter is easy - add up three sides of the rectangle, and the triangle.