Question 1:
21 cm, 17 cm and 10 cm
a = 21 cm
b = 17 cm
c = 10 cm
S =
=
Area =
= 3 x 7 x 2 x 2
= 84cm²
∴ The area of the triangle is 84cm².
Question 2:
42 cm, 39 cm and 45 cm
a = 42 cm
b =39 cm
c = 45 cm
=3 x 3 x 3 x 7 x 2 x 2
= 756cm²
∴ The area of the triangle is 756cm².
→ Heron's Formula
The area of a triangle of sides a, b and c is where semi-perimeter S is the half of the sum of all sides of the triangle. .
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Verified answer
Answers:
Question 1:
21 cm, 17 cm and 10 cm
a = 21 cm
b = 17 cm
c = 10 cm
S =![\dfrac{a+b+c}{2} \dfrac{a+b+c}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
=![\dfrac{21+17+10}{2}=\dfrac{48}{2}=24cm \dfrac{21+17+10}{2}=\dfrac{48}{2}=24cm](https://tex.z-dn.net/?f=%5Cdfrac%7B21%2B17%2B10%7D%7B2%7D%3D%5Cdfrac%7B48%7D%7B2%7D%3D24cm)
Area =![\sqrt{S(S-a)(S-b)(S-c)} \sqrt{S(S-a)(S-b)(S-c)}](https://tex.z-dn.net/?f=%5Csqrt%7BS%28S-a%29%28S-b%29%28S-c%29%7D)
=![\sqrt{24(24-21)(24-17)(24-10)} \sqrt{24(24-21)(24-17)(24-10)}](https://tex.z-dn.net/?f=%5Csqrt%7B24%2824-21%29%2824-17%29%2824-10%29%7D)
=![\sqrt{24\times3\times7\times14} \sqrt{24\times3\times7\times14}](https://tex.z-dn.net/?f=%5Csqrt%7B24%5Ctimes3%5Ctimes7%5Ctimes14%7D)
=![\sqrt{3\times8\times3\times7\times2\times7} \sqrt{3\times8\times3\times7\times2\times7}](https://tex.z-dn.net/?f=%5Csqrt%7B3%5Ctimes8%5Ctimes3%5Ctimes7%5Ctimes2%5Ctimes7%7D)
= 3 x 7 x 2 x 2
= 84cm²
∴ The area of the triangle is 84cm².
Question 2:
42 cm, 39 cm and 45 cm
a = 42 cm
b =39 cm
c = 45 cm
S =![\dfrac{a+b+c}{2} \dfrac{a+b+c}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
=![\dfrac{42+39+45}{2}=\dfrac{126}{2}=63cm \dfrac{42+39+45}{2}=\dfrac{126}{2}=63cm](https://tex.z-dn.net/?f=%5Cdfrac%7B42%2B39%2B45%7D%7B2%7D%3D%5Cdfrac%7B126%7D%7B2%7D%3D63cm)
Area =![\sqrt{S(S-a)(S-b)(S-c) \sqrt{S(S-a)(S-b)(S-c)](https://tex.z-dn.net/?f=%5Csqrt%7BS%28S-a%29%28S-b%29%28S-c%29)
=![\sqrt{63(63-42)(63-39)(63-45) \sqrt{63(63-42)(63-39)(63-45)](https://tex.z-dn.net/?f=%5Csqrt%7B63%2863-42%29%2863-39%29%2863-45%29)
=![\sqrt{63\times21\times24\times18 \sqrt{63\times21\times24\times18](https://tex.z-dn.net/?f=%5Csqrt%7B63%5Ctimes21%5Ctimes24%5Ctimes18)
=![\sqrt{9\times7\times7\times3\times3\times8\times9\times2 \sqrt{9\times7\times7\times3\times3\times8\times9\times2](https://tex.z-dn.net/?f=%5Csqrt%7B9%5Ctimes7%5Ctimes7%5Ctimes3%5Ctimes3%5Ctimes8%5Ctimes9%5Ctimes2)
=![3\times3\times3\times7\sqrt{2\times4\times2 3\times3\times3\times7\sqrt{2\times4\times2](https://tex.z-dn.net/?f=3%5Ctimes3%5Ctimes3%5Ctimes7%5Csqrt%7B2%5Ctimes4%5Ctimes2)
=3 x 3 x 3 x 7 x 2 x 2
= 756cm²
∴ The area of the triangle is 756cm².
Knowledge Bytes:
→ Heron's Formula
The area of a triangle of sides a, b and c is
where semi-perimeter S is the half of the sum of all sides of the triangle.
.