The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.

Correct result:

h = 14
o = 70

Solution:

a : b : c : d = 2 : 5 : 8 : 5 a = 8 x b = d = 5 x c = 2 x a ∣ ∣ c S = 245 h = \sqrt{d^{2} - ((a - c) / 2)^{2}} h = x \cdot \sqrt{5^{2} - ((8 - 2) / 2)^{2}} h = x \cdot \sqrt{5^{2} - ((8 - 2) / 2)^{2}} h = x \cdot \sqrt{16} h = 4 x S = \frac{a + c}{2} h S = \frac{8 x + 2 x}{2} h S = \frac{8 x + 2 x}{2} \cdot 4 x S = 5 x \cdot 4 x x = \sqrt{S / 20} = \sqrt{245 / 20} = \frac{7}{2} = 3.5 h = 4 \cdot x = 4 \cdot 3.5 = 14

a = 8 \cdot x = 8 \cdot 3.5 = 28 b = 5 \cdot x = 5 \cdot 3.5 = \frac{35}{2} = 17.5 d = 5 \cdot x = 5 \cdot 3.5 = \frac{35}{2} = 17.5 c = 2 \cdot x = 2 \cdot 3.5 = 7 S_{1} = \frac{a + c}{2} \cdot h = \frac{28 + 7}{2} \cdot 14 = 245 S_{1} = S o = a + b + c + d = 28 + 17.5 + 7 + 17.5 = 70

Try another example

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Showing 1 comment:

Math student

I don't understand.

1 year ago Like

Tips to related online calculators

Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1 video2

Next similar math problems:

Trapezoid
Area of trapezoid is 135 cm². Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
ISO trapezoid v2
bases of Isosceles trapezoid measured 20 cm and 4 cm and its perimeter is 55 cm. What is the are of a trapezoid?
Right isosceles
Calculate area of the isosceles right triangle which perimeter is 26 cm.
Right triangle
Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
Trapezoid 15
Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
Ratio in trapezium
The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
In a
In a right triangle, the areas of the squares above its sides are 169; 25 and 144. The length of its longer leg is:
R Trapezium
Rectangular trapezium has bases 12 and 5 and area 84 cm². What is its perimeter?
Flowerbed 2
Around the square flower bed in a park is sidewalk 2 m wide. The area of this sidewalk is 243 m². What is the area of the flowerbed?
The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
Area 4gon
Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°.
Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm². Calculate content of square over the triangle's hypotenuse.
Triangle SAS
Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
Trapezium
The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm². Calculate the length of the base and the height of the trapezoid.
Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc