# Day 3 E. Engagement (Time Frame: Learning Task 2: Read And A…

Day 3 E. Engagement (Time Frame: Learning Task 2: Read and analyze each problem below then answer the questions that follow. 1. Consider the trapezoid on the right. If you cut the trapezoid along the dotted lines, you divide it into two figures. Now, answer the following questions: b₁ 20 cm – Into what shapes has the trapezoid been divided? – What are the height and base of each shape? – Find the area of each shape and add them together. -How does this sum compare to the area of the trapezoid? h 16 cm bz 25 cm

**Answer:**

**Step-by-step explanation:**

– The trapezoid has been divided into a rectangle and a right triangle.

– The height and base of the rectangle are 20 cm and 25 cm, respectively. The height and base of the right triangle are 16 cm and (25-20)=5 cm, respectively.

– The area of the rectangle is (20 cm) x (25 cm) = 500 cm². The area of the right triangle is 1/2 x (5 cm) x (16 cm) = 40 cm². Adding these areas together, we get 540 cm².

– To compare this sum to the area of the trapezoid, we need to find the area of the trapezoid. The formula for the area of a trapezoid is: A = (1/2) x (b₁ + b₂) x h, where b₁ and b₂ are the lengths of the parallel bases, and h is the height. Plugging in the given values, we get: A = (1/2) x (20 cm + 25 cm) x 16 cm = 420 cm². Therefore, the sum of the areas of the rectangle and right triangle is greater than the area of the trapezoid.