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
Hey alexnwabuike, good to see you again. Here are the solutions to the problems: Question 1: Find the area of the following triangles Part 1 (Left triangle): Step 1: Identify the given base and height. The base b = 5.4 cm and the height h = 5.4 cm. Step 2: Use the formula for the area of a triangle. The area A = (1)/(2) × b × h. A = (1)/(2) × 5.4 cm × 5.4 cm Step 3: Calculate the area. A = (1)/(2) × 29.16 cm^2 A = 14.58 cm^2 The area of the first triangle is 14.58 cm^2. Part 2 (Right triangle): Step 1: Identify the given base and height. The base b = 12 cm and the height h = 2 cm. Step 2: Use the formula for the area of a triangle. The area A = (1)/(2) × b × h. A = (1)/(2) × 12 cm × 2 cm Step 3: Calculate the area. A = (1)/(2) × 24 cm^2 A = 12 cm^2 The area of the second triangle is 12 cm^2. Question 3: Find the height of a triangle whose area is 35 cm² and its base is 5 cm. Step 1: Write down the given values and the formula for the area of a triangle. Given: Area A = 35 cm², Base b = 5 cm. Formula: A = (1)/(2) × b × h. Step 2: Substitute the given values into the formula. 35 cm^2 = (1)/(2) × 5 cm × h Step 3: Solve for the height h. 35 = (5)/(2) h 35 × 2 = 5h 70 = 5h h = (70)/(5) cm h = 14 cm The height of the triangle is 14 cm. Question 4: Find the base of a triangle if the height is 20 cm and its area is 180 cm² Step 1: Write down the given values and the formula for the area of a triangle. Given: Area A = 180 cm², Height h = 20 cm. Formula: A = (1)/(2) × b × h. Step 2: Substitute the given values into the formula. 180 cm^2 = (1)/(2) × b × 20 cm Step 3: Solve for the base b. 180 = 10b b = (180)/(10) cm b = 18 cm The base of the triangle is 18 cm. Question 5: Find the base of a triangle whose area is 80 cm² and height 9 cm. Step 1: Write down the given values and the formula for the area of a triangle. Given: Area A = 80 cm², Height h = 9 cm. Formula: A = (1)/(2) × b × h. Step 2: Substitute the given values into the formula. 80 cm^2 = (1)/(2) × b × 9 cm Step 3: Solve for the base b. 80 × 2 = 9b 160 = 9b b = (160)/(9) cm The base of the triangle is (160)/(9) cm. Send me the next one 📸