Find the area of the shape.
1 answer:
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Answer:
√190
Step-by-step explanation:
In the figure , there are 2 right angled triangles with a common perpendicular & both the triangles combine to form a new right angled triangle.
Let the triangle with 9 as base be T¹ & Let the triangle with base 10 be T². Let the triangle formed by T¹ & T² be T³.
In T² ,
Hypotenuse = y
Base = 10
According to Pythagorean Theorem ,
(Hypotenuse)² = (Base)² + (Perpendicular)²
Hence, (Perpendicular)² =
In T¹ ,
Perpendicular = (∵ Both T¹ & T² have common perpendicular)
⇒(Perpendicular)² =
Base = 9
⇒ (Base)² = 9²
Hypotenuse =
Using Pythagorean Theorem ,
(Hypotenuse)² = (Perpendicular)² + (Base)²
⇒ (Hypotenuse)² = .............................................eqn.2
Now in T³ ,
Base = y
⇒ (Base)² = y²
Perpendicular = (∵Perpendicular of T³ = Hypotenuse of T²)
⇒ (Perpendicular)² =
Hypotenuse = 9 + 10 = 19
Using Pythagorean Theorem ,
(Hypotenuse)² = (Perpendicular)² + (Base)²