Find the area of the quadrilateral ABCD in which AB=17 cm,AD=9cm,CD=12cm,angle ACB =90 and BC=8cm - Maths - Perimeter and Area

Question

Find the area of the quadrilateral ABCD in which AB=17
cm,AD=9cm,CD=12cm,angle ACB =90?and BC=8cm

Sneha Apar · Accepted Answer

Dear student,

So, perimeter of ABCD = AB + BC + CD + AD = 17 cm + 8 cm + 12 cm + 9 cm = 46 cm $Also are of Δ ABC = \frac{1}{2} \times AC \times BC = \frac{1}{2} \times 15 cm \times 8 cm = 60 {cm}^{2}$ and In ΔAC D $semiperimeter = \frac{15 cm+9 cm + 12 cm}{2} = 18 cm ∴ Area of Δ ACD = \sqrt{18 cm (18 cm - 15 cm) (18 cm - 9 cm) (18 cm - 12 cm)} = \sqrt{18 cm \times 3 cm \times 9 cm \times 6 cm} = 54 {cm}^{2}$ Hence area of ABCD = Area (ABC) + Area (ACD) = 60 cm2 + 54 cm2 = 114 cm2 Regards

Find the area of the quadrilateral ABCD in which AB=17 cm,AD=9cm,CD=12cm,angle ACB =90?and BC=8cm.