Find the area of quadrilateral in which the length of one of its diagonal is 36cm and perpendicular drawn to it from the opposite vertices are 10.5 cm and 5.5 cm respectively.
Answers
Step-by-step explanation:
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Given,
The length of one of its diagonal of a quadrilateral = 36 cm
The length of the perpendiculars drawn to the diagonal from the opposite vertices is 10.5 cm and 5.5 cm respectively.
To find,
The area of the quadrilateral.
Solution,
We can simply solve this mathematical problem using the following process:
Mathematically,
The area of a quadrilateral
= 1/2 × (length of a diagonal) × (sum of the length of the perpendiculars drawn to the diagonal from the opposite vertices){Statement-1}
Now, according to the question;
The area of the quadrilateral
= 1/2 × (length of a diagonal) × (sum of the length of the perpendiculars drawn to the diagonal from the opposite vertices)
= 1/2 × (36 cm) × (10.5 cm + 5.5 cm)
= 1/2 × (36 cm) × 16 cm
= 288 cm^2
Hence, the area of the quadrilateral is equal to 288 cm^2.