1.2: Real Life Geometry 1.1.The pleture below is of bridge made out of steel. Each section of the bridge is triangle, 3 metres wide, 4 metres high and a slant height of 5 m . How much steel is needed to create each section of the bridge? What do we call a triangle with these measurements? How many triangles are found in the design of one complete side panel? Calculate the amount of steel that is needed for one side panel of the bridge? (2)

To find the amount of steel needed to create each section of the bridge, we need to calculate the area of each triangular section. The formula for the area of a triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Given that each section of the bridge is a triangle with a base of 3 meters, a height of 4 meters, and a slant height of 5 meters, we can calculate the area of each section. 1. Calculate the area of each triangular section: \[ \text{Area} = \frac{1}{2} \times 3 \times 4 = 6 \text{ square meters} \] 2. Determine the type of triangle with these measurements: A triangle with a base of 3 meters, a height of 4 meters, and a slant height of 5 meters is a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the lengths of the other two sides (base and height). 3. Calculate the number of triangles in one complete side panel: Since each section of the bridge is a triangle, and the bridge is made up of multiple sections, we need to determine how many triangles are in one complete side panel. This will depend on the design of the bridge. 4. Calculate the amount of steel needed for one side panel of the bridge: To calculate the amount of steel needed for one side panel of the bridge, we need to multiply the area of each triangular section by the number of triangles in one complete side panel. Let's calculate the amount of steel needed for one side panel of the bridge. Calculate the value by following steps: - step0: Calculate: \(6\times 2\) - step1: Multiply the numbers: \(12\) The amount of steel needed for one side panel of the bridge is 12 square meters.