Isosceles trapezoid 3

In isosceles trapezoid ABCD, calculate the unknown side length "a" and its area. Sides b = d = 50 cm, c = 20 cm, and the height = 48 cm.

Final Answer:

a =  48 cm
S =  1632 cm2

Step-by-step explanation:

b=50 cm d=50 cm c=20 cm v=48 cm  v2 = x2+b2 x=b2−v2​=502−482​=14 cm a=c+2⋅ x=20+2⋅ 14=48 cm
S=2a+c​⋅ v=248+20​⋅ 48=1632 cm2

Try another example


Help us improve! If you spot a mistake, please let let us know. Thank you!



Showing 1 comment:
Dr. Math
To solve for the unknown side length a and the area of the isosceles trapezoid ABCD , follow these steps:

Given:


- Sides b = d = 50 cm
- Side c = 20 cm
- Height h = 48 cm

Step 1:

Find the unknwon side length a
In an isosceles trapezoid, the two non-parallel sides ( b and d ) are equal. The formula to find the unknown base a is:

a = c + 2x


Where x is the horizontal projection of the non-parallel side. Using the Pythagorean theorem:

x = √b2 - h2 = √502 - 482 = √2500 - 2304 = √196 = 14 cm


Now, substitute x into the formula for a :

a = c + 2x = 20 + 2(14) = 20 + 28 = 48 cm

Step 2:

Calculate the area
The area A of a trapezoid is given by:

A = 12 × (a + c) × h


Substitute the known values:

A = 12 × (48 + 20) × 48 = 12 × 68 × 48 = 34 × 48 = 1632 cm2

Final Answer:


- Unknown side length a = 48 cm
- Area A = 1632 cm2





Tips for related online calculators
See also our right triangle calculator.
Calculation of an isosceles triangle.
See also our trigonometric triangle calculator.

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

algebraarithmeticplanimetry

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

Related math problems and questions: