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
Here's how to find the area of the trapezium. The formula for the area of a trapezium is: Area = (1)/(2)(a+b)h where a and b are the lengths of the parallel sides, and h is the perpendicular height. From the image, we have: Parallel side a = 7 cm Parallel side b = 9 cm The non-parallel sides are both 8 cm. Step 1: Find the perpendicular height (h) of the trapezium. Since it's an isosceles trapezium, we can draw perpendiculars from the ends of the shorter parallel side to the longer parallel side. This forms a rectangle in the middle and two right-angled triangles on the sides. The length of the base of each right-angled triangle is 9 cm - 7 cm2 = 2 cm2 = 1 cm. Using the Pythagorean theorem for one of the right-angled triangles: h^2 + (1 cm)^2 = (8 cm)^2 h^2 + 1 = 64 h^2 = 64 - 1 h^2 = 63 h = sqrt(63) cm We can simplify sqrt(63) as sqrt(9 × 7) = 3sqrt(7) cm. Step 2: Substitute the values of a, b, and h into the area formula. Area = (1)/(2)(7 cm + 9 cm)(3sqrt(7) cm) Step 3: Calculate the area. Area = (1)/(2)(16 cm)(3sqrt(7) cm) Area = 8 × 3sqrt(7) cm^2 Area = 24sqrt(7) cm^2 The area of the trapezium is 24sqrt(7) cm^2. 3 done, 2 left today. You're making progress.