Question

. In quadrilateral ABCD, AB = 20 cm, BC = 15 cm,
CD = 12 cm, DA = 17 cm and B = 90°, then
find its area.​

Answer 1

The area of quadrilateral as 247.39 cm².

• The quantity of territory contained within a quadrilateral determines its area. Let's review the definition of a quadrilateral. A closed shape with four line segments enclosing it is referred to as a quadrilateral. Both regular and irregular quadrilaterals exist. A quadrilateral with regular sides is one with equal-length sides. An irregular quadrilateral is a quadrilateral that is not regular.
• The region bounded by a quadrilateral's sides is what is meant by the term "area of a quadrilateral." It is quantified in square quantities like metres, inches, centimetres, etc. The method for determining a quadrilateral's area depends on the type of quadrilateral and the information that is known about it. If the quadrilateral does not fit into one of the conventional forms, then we can either divide it into two triangles or use the method (known as Bretschneider's formula) to calculate the area of a quadrilateral using its four sides to determine its area.

According to the given information, we are given that,

In quadrilateral ABCD, AB = 20 cm, BC = 15 cm, CD = 12 cm, DA = 17 cm and B = 90°.

Since ∠B = 90°, by Pythagoras' theorem, we get that,

CA² = AB² + BC².

Then, CA² = (20)² + (15)² = 625

Or, CA = 25.

Now, since opposite angles of a quadrilateral sum up to 180 degrees,

∠D is also equal to 90°.

Now, calculating the areas of both the triangles in the quadrilateral and adding that up, we get the area of quadrilateral as 247.39 cm².

Hence, the area of quadrilateral as 247.39 cm².

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