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Traffic Triangle Area Calculation

Calculate the area of a traffic triangle formed at the intersection of three streets using Heron's formula. Find step-by-step solutions for different examples.

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Traffic Triangle Area Calculation

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  1. The intersection of three streets forms a piece of land called a traffic triangle. Find the area of the traffic triangle shown. STEP 1 Find the semiperimeter s. 1 1 s = (a + b + c ) = (170 + 240 + 350) 2 2 EXAMPLE 4 Solve a multi-step problem Urban Planning SOLUTION = 380

  2. STEP 2 Use Heron’s formula to find the area of ABC. Area = 18,300 = 380 (380 – 170) (380 – 240) (380 – 350) s (s – a)(s – b)(s – c) EXAMPLE 4 Solve a multi-step problem The area of the traffic triangle is about 18,300 square yards.

  3. Find the area of ABC. 4. STEP 1 Find the semiperimeter s. 1 1 s = (a + b + c ) = (5 + 8 + 11) 2 2 for Example 4 GUIDED PRACTICE SOLUTION = 12

  4. STEP 2 Use Heron’s formula to find the area of ABC. Area = 18.3 = 12 (12 – 8) (12 – 11) (12 – 5) s (s – a)(s – b)(s – c) for Example 4 GUIDED PRACTICE The area is about 18.3 square units.

  5. Find the area of ABC. 5. STEP 1 Find the semiperimeter s. 1 1 2 2 s = (a + b + c ) = (4 + 9+ 7) for Example 4 GUIDED PRACTICE SOLUTION = 10

  6. STEP 2 Use Heron’s formula to find the area of ABC. Area = 13.4 = 10 (10– 4) (10 – 9) (10 – 7) s (s – a)(s – b)(s – c) for Example 4 GUIDED PRACTICE The area is about 13.4 square units.

  7. Find the area of ABC. 6. STEP 1 Find the semiperimeter s. 1 1 2 2 s = (a + b + c ) = (15 + 23+ 127) for Example 4 GUIDED PRACTICE SOLUTION = 25

  8. STEP 2 Use Heron’s formula to find the area of ABC. Area = 80.6 = 25 (25– 15) (25 – 23) (25 – 12) s (s – a)(s – b)(s – c) for Example 4 GUIDED PRACTICE The area is about 80.6 square units.

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