Isosceles trapezoid 3

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

Correct 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

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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 = \sqrt{b2 - h2} = \sqrt{502 - 482} = \sqrt{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 = 1/2 × (a + c) × h


Substitute the known values:

A = 1/2 × (48 + 20) × 48 = 1/2 × 68 × 48 = 34 × 48 = 1632 cm2

Final Answer:


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





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