Verified answer

Let the sides of quadrilateral be A, B, C, and D cm.

Given:-

• length of one diagonal of quadrilateral (BD) = 10cm
• lengths of the perpendiculars drawn from it on other vertices = 4cm and 4.5cm.

Solution :-

Now, according to our question,

Area of quadrilateral ABCD = 1/2 × length of one diagonal × sum of the lengths of the perpendiculars that are drawn from it on the other vertices.

⇒Area of quadrilateral = 1/2 × 10cm × ( 4 + 4.5)cm

⇒Area of quadilateral = 1/2 × 10cm × 8.5cm

⇒Area of quadrilateral = 85/2cm²

⇒Area of quadrilateral = 42.5cm²

Therefore, area of given quadrilateral is 42.5cm².

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NOTE:-

• If the length of diagonal and the length of the perpendiculars from the vertices are given, then area of quadilateral can be calculated.
• Formula for Area of quadrilateral = 1/2 × length of one diagonal × sum of the lengths of the perpendiculars that are drawn from it on the other vertices.

Answer:

Given :-

• A quadrilateral whose diagonal is 10 cm and perpendicular on its diagonal from opposite vertices 4 cm and 4.5 cm.

To Find :-

• What is the area of the quadrilateral.

Formula Used :-

✪ Area of quadrilateral = ½ × Diagonal length × Sum of length of perpendicular ✪

Solution :-

Given :

• Diagonal = 10 cm
• Sum of length = 4 cm and 4.5 cm

According to the question by using the formula we get,

⇒ Area of quadrilateral = ½ × 10 × 4 + 4.5

⇒ Area of quadrilateral = ½ × 10 × 8.5

⇒ Area of quadrilateral = ½ × 85

➠ Area of quadrilateral = 42.5 cm²

∴ The area of the quadrilateral is 42.5 cm² .