### 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.

**Answer:**

180 cm^{2}

**Step by Step Explanation:**

- 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.
- Let's draw the diagonal AC in the quadrilateral ABCD,

The area of the right triangle ABC =

× AB × BC1 2

=

× 8 × 151 2

= 60 cm^{2}. - AC = ^@\sqrt{ AB^2 + BC^2 }^@

= ^@\sqrt{ 8^2 + 15^2 }^@

= 17 cm - The area of the triangle ACD can be calculated using Heron's formula.

S =CD + DA + AC 2

=16 + 17 + 17 2

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

= √ 25(25 - 16)(25 - 17)(25 - 17)

= 120 cm^{2} - The area of the quadrilateral ABCD = Area(ABC) + Area(ACD) = 60 + 120 = 180 cm
^{2}.