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:
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Dr. Math
To solve for the unknown side length a and the area of the isosceles trapezoid ABCD , follow these steps:
- Sides b = d = 50 cm
- Side c = 20 cm
- Height h = 48 cm
In an isosceles trapezoid, the two non-parallel sides ( b and d ) are equal. The formula to find the unknown base a is:
Where x is the horizontal projection of the non-parallel side. Using the Pythagorean theorem:
Now, substitute x into the formula for a :
The area A of a trapezoid is given by:
Substitute the known values:
- Unknown side length a = 48 cm
- Area A = 1632 cm2
Given:
- Sides b = d = 50 cm
- Side c = 20 cm
- Height h = 48 cm
Step 1:
Find the unknwon side length aIn 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 areaThe 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
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