Question 8 - Figure it out - Page 169-170 - Chapter 7 Class 8 - Area (Ganita Prakash II)

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Question 8 ZYXW is a trapezium with ZY‖WX. A is the midpoint of XY. Show that the area of the trapezium ZYXW is equal to the area of ΔZWB.Let’s look at the answer in detail Trapezium to Triangle Show that Area of Trapezium ZYXW = Area of . STEP 1 OF 6 Step 1: Identifying the Midpoint Look at and . Point is the midpoint of , so XA. Previous Next StepTrapezium to Triangle Show that Area of Trapezium ZYXW = Area of . STEP 2 OF 6 Step 2: Angles & Congruence Let's prove they are congruent using the ASA (Angle-Side-Angle) rule: Angle (Red): Vertically opposite angles at A are equal. Side (Ticks): ( A is the midpoint). Angle (Blue): Since , the alternate interior angles at Y and X are equal. Because of ASA, . Previous Next StepTrapezium to Triangle Show that Area of Trapezium ZYXW = Area of IWB. STEP 3 OF 6 Step 3: Equal Area Since they are congruent, they have the exact same area. Previous Next StepTrapezium to Triangle Show that Area of Trapezium ZYXW = Area of . STEP 4 OF 6 Step 4: Trapezium Composition The Trapezium ZYXW is made of the quadrilateral . Previous Next Step Trapezium to Triangle Show that Area of Trapezium ZYXW = Area of . STEP 5 OF 6 Step 5: Triangle Composition The large triangle is made of the exact same quadrilateral . Previous Next Step Trapezium to Triangle Show that Area of Trapezium ZYXW = Area of . STEP 6 OF 6 Conclusion Since we just replaced one equal triangle with another, the total areas must be the same! Trapezium Triangle ZWB =ZWXA + AXAB Area(ZYXW) = Area( ZWB) Previous Restart Proof