Studdy AI Logo
Math  /  Geometry

QuestionFind the area KK of the triangle specified below. a=3,b=10,c=12a=3, b=10, c=12
The area KK is □\square square units. (Do not round until the final answer. Then round to two decimal places as needed.)

Studdy Solution

STEP 1

1. We are given the side lengths of a triangle: a=3 a = 3 , b=10 b = 10 , c=12 c = 12 .
2. We need to find the area K K of the triangle.
3. We will use Heron's formula to find the area of the triangle.

STEP 2

1. Calculate the semi-perimeter of the triangle.
2. Apply Heron's formula to find the area of the triangle.
3. Round the final answer to two decimal places.

STEP 3

Calculate the semi-perimeter s s of the triangle using the formula:
s=a+b+c2 s = \frac{a + b + c}{2}
Substitute the given side lengths:
s=3+10+122 s = \frac{3 + 10 + 12}{2}

STEP 4

Simplify the expression to find s s :
s=252 s = \frac{25}{2} s=12.5 s = 12.5

STEP 5

Apply Heron's formula to find the area K K of the triangle:
K=s(s−a)(s−b)(s−c) K = \sqrt{s(s-a)(s-b)(s-c)}
Substitute the values of s s , a a , b b , and c c :
K=12.5(12.5−3)(12.5−10)(12.5−12) K = \sqrt{12.5(12.5 - 3)(12.5 - 10)(12.5 - 12)}

STEP 6

Simplify the expression inside the square root:
K=12.5×9.5×2.5×0.5 K = \sqrt{12.5 \times 9.5 \times 2.5 \times 0.5}

STEP 7

Calculate the product:
K=12.5×9.5×2.5×0.5 K = \sqrt{12.5 \times 9.5 \times 2.5 \times 0.5} K=148.4375 K = \sqrt{148.4375}

STEP 8

Calculate the square root and round the final answer to two decimal places:
K≈148.4375 K \approx \sqrt{148.4375} K≈12.18 K \approx 12.18
The area K K of the triangle is approximately:
12.18 \boxed{12.18}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord