Question

Areas of Triangles and Quadril
28. Find the perimeter and area of the
ZBAC = 90°, AC = 20 cm, CD = 42 cm and
AD = 34 cm.
quadrilateral ABCD in which AB = 21 cm,​

Answer 1

Answer:

Step-by-step explanation:

Perimeter of quadrilateral ABCD is 126 cm and area of quadrilateral ABCD is 384 sq. cm.

In ΔABC ,

AC = 20 cm , AB = 21 cm and ∠CAB = 90°.

Therefore , By Pythagoras Theorem

BC² = AC² + AB²

BC² = 20² + 21² = 400+441 = 841

BC = 29 cm

Now Perimeter of quadrilateral ABCD = AB + BC + CD + AD

Perimeter = 21+29+42+34 = 126 cm.

Now area of quadrilateral ABCD is equal to Area of ΔABC + Area of ΔCAD .

Now area of ΔABC =  = 20 × 21 / 2 = 210 sq cm.

Area of ΔCAD =    , Using Heron's formula

Now s = (a+b+c)/2 = (42+34+20)/2 = 48 sq cm.

Now, area =  =  =  = 336 sq. cm

Now area of quadrilateral ABCD = Area of ΔABC + Area of ΔCAD

Area of quadrilateral ABCD = 48 + 336 = 384 sq cm.