Question

area of quadrilateral where two triangles are construct with AB as a base 40cm and AD as 9cm and sides have 15cm and 28cm​

Answer 1

let me know ur class level

Answer 2

Answer:

306 sq. cm

Step-by-step explanation:

//see the attached figure and read through the explanation

from Triangle ADB, use Pythagoras theorem to calculate the diagonal.

BD² = AB² + AD²

       = (40)² + (9)² = 1600 + 81 = 1681

BD = 41 cm.

Area of triangle ABD = 1/2 * AB * AD = 1/2 * 40 * 9 = 180 sq. cm.

Now in triangle CDB,

perimeter of CDB = 2s  = CD+ CB+ BD = 15 + 28 + 41 = 84 cm.

2s = 84 cm.

side = 42 cm.

using Heron's formula,

Area of CDB = √[s(s-a)(s-b)(s-c)]

                     = √42 * (42 -15)(42 - 28)(42 - 41)

                     =  126 sq.cm.

Area of quadrilateral = Triangle ABD + Triangle CDB

                                 = 180 + 126

                                 = 306 sq.cm.