Trapezoid ABCD, top and bottom are parallel. Left is 45, bottom is 60, right is 30, top is unknown.
Trapezoid EFGH is similar to ABCD, top and bottom are parallel. Top is 10, other sides are unknown.
Area of ABCD is 9 times larger than EFGH.
What is the perimeter of EFGH ?
EFGH is a square.angle E equal to x+6 and EF equal to x+1cm. Find the perimeter of EFGH
To find the perimeter of EFGH, we need to determine the lengths of all four sides of the trapezoid.
Let's start with trapezoid ABCD:
We know that the left side is 45 units, the bottom side is 60 units, and the right side is 30 units. The top side is unknown, so let's call it "x."
Since trapezoid ABCD is similar to trapezoid EFGH, we can set up a proportion to find the length of the top side of ABCD. The proportion can be set up as:
(top side of ABCD) / (top side of EFGH) = (bottom side of ABCD) / (bottom side of EFGH)
x / 10 = 60 / 10
x = 6
So, the length of the top side of ABCD is 6 units.
We also know that the area of ABCD is 9 times larger than the area of EFGH. The formula for the area of a trapezoid is (1/2) * (sum of the bases) * (height). Since the bases of EFGH are the top and bottom sides, and the height is unknown, we can use the proportion:
(area of ABCD) / (area of EFGH) = (sum of the bases of ABCD) / (sum of the bases of EFGH)
9 = (6 + x) / (10 + 10)
90 + 9x = 120
9x = 30
x = 30 / 9
x ≈ 3.33
Therefore, the length of the top side of EFGH is approximately 3.33 units.
Now, we can calculate the perimeter of EFGH. Since the opposite sides of a trapezoid are parallel, the lengths of the parallel sides (top and bottom) are added twice, and we also sum up the lengths of the non-parallel sides.
Perimeter of EFGH = 2 * (top side) + (left side) + (right side)
Perimeter of EFGH = 2 * 3.33 + 45 + 30
Perimeter of EFGH ≈ 6.66 + 45 + 30
Perimeter of EFGH ≈ 81.66
Therefore, the perimeter of EFGH is approximately 81.66 units.