Question

a park in the shape of a quadilateral ABCD Angle C is 90° AB is 9m BC is 12m CD= 5m and AD = 8m . how much area does it occupy ?​

Answer 1

Answer:

Diagonal BD divide it into two triangle.the area of the triangle BCD is 1/2×DC×BC

=1/2×5×12sqm

=30sqm

BD=√(5^2+12^2)=√(25+144)=√169=13

the area of the triangle ABD whose three sides are AB=9m,AD=8m,BD=13m

half of the perimeter is s=(9+8+13)/2m

=30/2m=15m

so area is √15(15-13)(15-9)(15-8)sqm

=√(15.2.6.7)sqm

=6√35sqm

do the total area of ABCD is

(30+6√35)sqm

Answer 2

Solution:

Given a quadrilateral ABCD in which ∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m & AD = 8 m.

Join the diagonal BD which divides quadrilateral ABCD in two triangles i.e ∆BCD & ∆ABD.

In ΔBCD,

By applying Pythagoras Theorem

BD²=BC² +CD²

BD²= 12²+ 5²= 144+25

BD²= 169

BD = √169= 13m

∆BCD is a right angled triangle.

Area of ΔBCD = 1/2 ×base× height

=1/2× 5 × 12= 30 m²

For ∆ABD,

Let a= 9m, b= 8m, c=13m

Now,

Semi perimeter of ΔABD,(s) = (a+b+c) /2

s=(8 + 9 + 13)/2 m

= 30/2 m = 15 m

s = 15m

Using heron’s formula,

Area of ΔABD = √s (s-a) (s-b) (s-c)

= √15(15 – 9) (15 – 9) (15 – 13)

= √15 × 6 × 7× 2

=√5×3×3×2×7×2

=3×2√35

= 6√35= 6× 5.92

[ √6= 5.92..]

= 35.52m² (approx)

Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD

= 30+ 35.5= 65.5 m²

Hence, area of the park is 65.5m²