Question

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ACB = 90° and AC = 15 cm.​

Answer 1

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We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and ∠ACB = 90∘.

We take a diagonal AC, where AC divides ABCD into two triangles ΔACB and ΔADC.

Since ∆ACB is right angled at C, we have

↪AC = 15 cm; AB = 17 cm

↪AB2 = AC2 + BC2

Area of right angled triangle ABC, say A1 is given by, where,

↪Base = BC = 8 cm;

↪Height = AC = 15 cm

Area of triangle ADC, say A2 having sides a, b, c and s as semi-perimeter is given by, where

↪a = AD = 9 cm;

↪b = DC = 12 cm;

↪ c = AC = 15 cm

Area of quadrilateral ABCD, say A

↪A = Area of ∆ACB + Area of ∆ADC

↪A = A¹+ A²

↪60+54

↪A = 114 cm²

Perimeter of quadrilateral ABCD, say P

↪P = 9 + 12 + 8 + 17

↪46 cm

Answer 2

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and ∠ACB = 90∘.

We take a diagonal AC, where AC divides ABCD into two triangles ΔACB and ΔADC.

Since ∆ACB is right angled at C, we have

↪AC = 15 cm; AB = 17 cm

↪AB2 = AC2 + BC2

Area of right angled triangle ABC, say A1 is given by, where,

↪Base = BC = 8 cm;

↪Height = AC = 15 cm

Area of triangle ADC, say A2 having sides a, b, c and s as semi-perimeter is given by, where

↪a = AD = 9 cm;

↪b = DC = 12 cm;

↪ c = AC = 15 cm

Area of quadrilateral ABCD, say A

↪A = Area of ∆ACB + Area of ∆ADC

↪A = A¹+ A²

↪60+54

↪A = 114 cm²

Perimeter of quadrilateral ABCD, say P

↪P = 9 + 12 + 8 + 17

↪46 cm