This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The problem asks to determine the area of triangle ABC, correct to one decimal place. The image shows a quadrilateral labeled ABCD with side lengths and a right angle. Step 1: Interpret the given diagram. The figure appears to be a rectangle with vertices B, A, C, D. The top side AB is labeled 120 cm. The left vertical side is labeled 60 cm. Although the label "60" is placed on the segment BD, the visual representation and the right angle symbol at D strongly suggest that the figure is a rectangle with sides 120 cm and 60 cm. In a rectangle, the side AD (or BC) would be the width. We will assume the width is 60 cm. The right angle symbol at D indicates that ADC = 90^, which is consistent with a rectangle. Step 2: Identify the dimensions of triangle ABC. In a rectangle, all angles are 90^. Therefore, B in triangle ABC is 90^. Triangle ABC is a right-angled triangle with base AB = 120 cm and height BC = 60 cm (since opposite sides of a rectangle are equal, BC = AD = 60 cm). Step 3: Calculate the area of triangle ABC. The area of a right-angled triangle is given by the formula: Area = (1)/(2) × base × height Substitute the values for triangle ABC: Area_ ABC = (1)/(2) × AB × BC Area_ ABC = (1)/(2) × 120 cm × 60 cm Area_ ABC = 60 × 60 cm^2 Area_ ABC = 3600 cm^2 Step 4: Round the answer to one decimal place. Area_ ABC = 3600.0 cm^2 3 done, 2 left today. You're making progress.