Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.

Result

S =  71.554 cm²

Solution:

$a:c=5:3 \ \\ b=6 \ \text{cm} \ \\ h=4 \ \text{cm} \ \\ x=\sqrt{ b^2-h^2 }=\sqrt{ 6^2-4^2 } \doteq 2 \ \sqrt{ 5 } \ \text{cm} \doteq 4.4721 \ \text{cm} \ \\ a=c + 2x \ \\ 3a=5c \ \\ 3 \cdot \ (c+2x)=5c \ \\ 3c + 6x=5c \ \\ 2c=6x \ \\ c=3 \cdot \ x=3 \cdot \ 4.4721 \doteq 6 \ \sqrt{ 5 } \ \text{cm} \doteq 13.4164 \ \text{cm} \ \\ a=5/3 \cdot \ c=5/3 \cdot \ 13.4164 \doteq 10 \ \sqrt{ 5 } \ \text{cm} \doteq 22.3607 \ \text{cm} \ \\ k_{1}=a/c - 5/3=22.3607/13.4164 - 5/3=0 \ \\ S=(a+c) \cdot \ h/2=(22.3607+13.4164) \cdot \ 4/2 \doteq 32 \ \sqrt{ 5 } \doteq 71.5542 \doteq 71.554 \ \text{cm}^2$

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. KLMN trapezoid
   The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
2. Median in right triangle
   In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
3. Liters od milk
   The cylinder-shaped container contains 80 liters of milk. Milk level is 45 cm. How much milk will in the container, if level raise to height 72 cm?
4. Book read
   If Petra read 10 pages per day, she would read the book two days earlier than she read 6 pages a day. How many pages does a book have?
5. Double ladder
   The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
6. Boxes
   200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
7. Elimination method
   Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
8. Stones 3
   Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
9. Guppies for sale
   Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na
10. Three unknowns
    Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
11. Trees
    Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
12. Linear system
    Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
13. Classroom
    There are eighty more girls in the class than boys. Boys are 40 percent and girls are 60 percent. How many are boys and how many girls?
14. Schools
    Three schools are attended by 678 pupils. To the first attend 21 students more and to the third 108 fewer students than to second school. How many students attend the schools?
15. Three brothers
    The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
16. Rabbits 3
    Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?
17. Two numbers
    We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.