I know number 13 is right, how do I do 11 and 12?
1 answer:
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Call the point of intersection of the diagonals point X.
Each base is the hypotenuse of an isosceles right triangle whose sides are the diagonals and whose 90° angle is at X. The altitude of that triangle (⊥ distance to the base from X) is half the length of the hypotenuse. Then the height of the trapezoid is half the sum of the base lengths.
The area of the trapezoid is the product of the height and half the sum of the base lengths, hence is the square of half the sum of the base lengths.
... Area = ((16 cm +30 cm)/2)² = (23 cm)² = 529 cm²
Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.
I've added the image of the ticket as an attachment.
(a) The missing side length
From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.
So, we have:
This gives
Collect like terms
Divide both sides by 4
(b) The length of the gold lines
There are 4 slant lines and the length of one of the slant lines is 5 cm (as calculated above).
So, the length of the gold line is:
(c) The number of gold ink bottles.
--- number of tickets
The length of all gold line in the 200 tickets is:
---- convert to meters
Given that:
--- 1 bottle for 20 m
The number of bottles (n) is:
Hence, 2 bottles of gold ink are enough.
Read more about perimeters at:
