A diagonal of a quadrilateral is 28cm . Two perpendicular drawn to it from opposite vertices are 10.2cm and 11.8cm .find the area of the quadrilateral .
Answers
The area of the quadrilateral is 308 cm².
Step-by-step explanation:
The diagonal of a quadrilateral, d = 28 cm
The length of the perpendiculars drawn to the diagonal from the opposite vertices are h₁ = 10.2 cm and h₂ = 11.8 cm
The formula of the area of a quadrilateral is given by,
Area = ½ * [diagonal] * [sum of the lengths of the perpendiculars drawn from the opposite vertices to the diagonal]
Now, substituting the given values in the above formula of the area we get,
Area of the quadrilateral = ½ * d * [h₁ + h₂]
⇒ Area of the quadrilateral = ½ * 28 * [10.2 + 11.8]
⇒ Area of the quadrilateral = ½ * 28 * 22
⇒ Area of the quadrilateral = 11 * 28
⇒ Area of the quadrilateral = 308 cm²
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