Question

find the area of quadrilateral ABCD in which AB=3cm,BC=4cm,CD = 4cm,DA=5cm,and AC=5cm​

Answer 1

Step-by-step explanation:

✓ area of quad. ABCD = area of triangle ABC + area of triangle ADC

✓ So.. area of triangle ABC using heron's formula =

s= a+b+c/2 = 3+4+5/2 = 12/2 = 6 cm

$\sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{6(6 - 3)(6 - 4)(6 - 5)}$

$\sqrt{6 \times 3 \times 2 \times 1}$

$\sqrt{2 \times 3 \times 3 \times 2 \times 1 \times 1}$

✓ 2 * 3 * 1 = 6cm²

✓ area of triangle ADC using heron's formula =

s = a+b+c/2 = 4 + 5 +5 /2 = 14/2 = 7cm

$\sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{7(7 - 4)(7 - 5)( 7 - 5)}$

$\sqrt{7 \times 3 \times 2 \times 2}$

2√21 cm²

✓ 2*4.58 = 9.16cm²

✓ now the area of quad is = 6+9.16 = 15.16cm²

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