SOLVE USING HERONS FORMULA 30 POINTS!!! the answer is 2√21 for triangle ADC but please find the root of 21 multiply it by 2 and give the answer please the correct answer will get a follow and will be marked brainliest
Answers
Answer:
15.2 cm²
Step-by-step explanation:
Let ABCD be the quadrilateral such that AB = 3cm, BC=4cm, CD=4cm, DA=5cm, AC=5cm.
(i)
In ΔABC, Semi-perimeter of ΔABC,
⇒ (3 + 4 + 5)/2
⇒ 6 cm.
Using Heron's formula:
Area of ΔABC = √s(s - a)(s - b)(s - c)
= √6(6 - 3)(6 - 4)(6 - 5)
= √6 * 3 * 2 * 1
= 6 cm²
(ii)
In ΔADC, Semi-perimeter of ΔADC,
⇒ (4 + 5 + 5)/2
⇒ 7 cm
Using Heron's formula:
Area of ΔADC = √s(s - a)(s - b)(s - c)
= √7(7 - 4)(7 - 5)(7 - 5)
= √7 * 3 * 2 * 2
= 84
= 2√21
= 2 * 4.6
= 9.2 cm².
(iii)
Area of Quadrilateral ABCD = Area of ΔABC + Area of ΔADC
⇒ 6 + 9.2
⇒ 15.2 cm²
Therefore, Area of Quadrilateral ABCD = 15.2 cm²
Hope it helps!