Exercise 4 - the line (AC) is perpendicular to the line (AB) - the line (EB) is perpendicular to the line (AB) - the lines (AE) and (BC) intersect at D - AC = 2.4 cm; BD = 2.5 cm: DC = 1.5 cm Determine the area of triangle ABE.

Identify the Right Angles: AC is perpendicular to AB EB is perpendicular to AB This implies that triangle ABC is a right triangle. Find Lengths: AC = 2.4 cm BD = 2.5 cm DC = 1.5 cm Use the Pythagorean Theorem in Triangle ABC: Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of AB. AC^2 + BC^2 = AB^2 (2.4)^2 + (2.5)^2 = AB^2 5.76 + 6.25 = AB^2 12.01 = AB^2 AB ≈ sqrt(12.01) AB ≈ 3.47 cm Calculate the Area of Triangle ABE: The area of a triangle is given by the formula: Area = (1/2) * base * height In this case, the base is AB and the height is DC. Area = (1/2) * AB * DC ≈ (1/2) * 3.47 cm * 1.5 cm ≈ 2.60 square cm The area of triangle ABE is approximately 2.60 square centimeters.