### Find the area of a quadrilateral whose sides are 8 cm, 15 cm, 16 cm and 17 cm and the angle between first two sides is a right angle.

180 cm2

Step by Step Explanation:
1. Let's ABCD is the quadrilateral with AB = 8 cm, BC = 15 cm, CD = 16 cm, DA = 17 cm, and angle ∠ABC = 90°, as shown in the following figure.
2. Let's draw the diagonal AC in the quadrilateral ABCD,

The area of the right triangle ABC =
 1 2
× AB × BC
=
 1 2
× 8 × 15
= 60 cm2.
3. AC = $\sqrt{ AB^2 + BC^2 }$
= $\sqrt{ 8^2 + 15^2 }$
= 17 cm
4. The area of the triangle ACD can be calculated using Heron's formula.
S =
 CD + DA + AC 2

=
 16 + 17 + 17 2

= 25 cm
5. The area of the triangle ACD = √ S(S - CD)(S - DA)(S - AC)

= √ 25(25 - 16)(25 - 17)(25 - 17)
= 120 cm2
6. The area of the quadrilateral ABCD = Area(ABC) + Area(ACD) = 60 + 120 = 180 cm2.

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