Question

find the area of the figure below by first finding the areas of the rectangle and triangles.
area of the rectangle: square square units
area of the triangle on the top: square square units
area of the triangle on the bottom: square square units
area of the figure: square square units

Explanation:

Step1: Determine the rectangle's dimensions

Assume the rectangle has a width of \( w \) and height of \( h \). From the grid (assuming each square is 1 unit), let's say the rectangle is 4 units wide and 6 units tall. So area of rectangle \( A_{rect} = w \times h = 4 \times 6 = 24 \) square units.

Step2: Area of top triangle

The top triangle has a base equal to the width of the rectangle (4 units) and height, say, 3 units. Area of triangle \( A_{tri - top} = \frac{1}{2} \times base \times height = \frac{1}{2} \times 4 \times 3 = 6 \) square units.

Step3: Area of bottom triangle

The bottom triangle is congruent to the top triangle (same base and height). So \( A_{tri - bottom} = \frac{1}{2} \times 4 \times 3 = 6 \) square units.

Step4: Total area of the figure

Sum the areas: \( A_{total} = A_{rect} + A_{tri - top} + A_{tri - bottom} = 24 + 6 + 6 = 36 \) square units.

Answer:

Area of the rectangle: \( 24 \) square units
Area of the triangle on the top: \( 6 \) square units
Area of the triangle on the bottom: \( 6 \) square units
Area of the figure: \( 36 \) square units