Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-a = 13.6 cm b = 18.4 cm
C = 15.3 cm
A) $108 \mathrm {~cm} ^ { 2 }$
B) $102 \mathrm {~cm} ^ { 2 }$
C) $105 \mathrm {~cm} ^ { 2 }$
D) $111 \mathrm {~cm} ^ { 2 }$

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-a = 13.6 cm b = 18.4 cm
C = 15.3 cm 
A) $108 \mathrm {~cm} ^ { 2 }$
B) $102 \mathrm {~cm} ^ { 2 }$
C) $105 \mathrm {~cm} ^ { 2 }$
D) $111 \mathrm {~cm} ^ { 2 }$

Quizplus · Accepted Answer

To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula. First, calculate the semi-perimeter (s) of the triangle: $s = \frac{a + b + c}{2}$. Then, the area (A) can be found using the formula: $A = \sqrt{s(s - a)(s - b)(s - c)}$.Given: $a = 13.6 \, \text{cm}, b = 18.4 \, \text{cm}, c = 15.3 \, \text{cm}$.1. Calculate the semi-perimeter: $s = \frac{13.6 + 18.4 + 15.3}{2} = 23.65 \, \text{cm}$.2. Calculate the area using Heron's formula: $A = \sqrt{23.65(23.65 - 13.6)(23.65 - 18.4)(23.65 - 15.3)}$.After performing the calculations, the area is approximately $102 \, \text{cm}^2$, which corresponds to choice B.

Find the Area of Triangle ABC with the Given Parts 108 cm2108 \mathrm {~cm} ^ { 2 }108 cm2

Find the Area of Triangle ABC with the Given Parts $108 \mathrm {~cm} ^ { 2 }$