Question

trapezoid:
a = box + box + box = box cm²
each triangle:
a = \frac{1}{2}bh
= \frac{1}{2} \times box \times 8
= box cm²
rectangle:
a = lw
= box \times 8
= box cm²

Explanation:

Step1: Calculate area of one triangle

The base of each triangle is \( 21 - 9 = 12 \)? Wait, no, looking at the diagram, the side length is 21 cm, the top and bottom sides of the trapezoid: wait, the trapezoid can be divided into a rectangle and two triangles? Wait, no, the diagram shows a trapezoid with height 8 cm, one base 9 cm, and the non - parallel side? Wait, maybe the trapezoid is composed of a rectangle (length 9 cm, height 8 cm) and two triangles (each with base \( \frac{21 - 9}{2}=6 \) cm, height 8 cm). Wait, the "Each triangle" part: the formula for the area of a triangle is \( A=\frac{1}{2}bh \). The base \( b \) of each triangle: from the diagram, the total length of the non - parallel side? Wait, the vertical side? Wait, the length of the triangle's base: the difference between 21 and 9 is \( 21 - 9 = 12 \), so each triangle has a base of \( \frac{12}{2}=6 \) cm, and height \( h = 8 \) cm.

So for one triangle:
\( A=\frac{1}{2}bh=\frac{1}{2}\times6\times8 \)
\(=\frac{1}{2}\times48 = 24\) \( cm^{2} \)

Step2: Calculate area of the rectangle

The rectangle has length \( l = 9 \) cm and width \( w = 8 \) cm. The formula for the area of a rectangle is \( A=lw \), so \( A = 9\times8=72 \) \( cm^{2} \)

Step3: Calculate area of the trapezoid

The trapezoid is composed of 2 triangles and 1 rectangle. So the area of the trapezoid \( A=24 + 72+24 \) (since there are two triangles, each with area 24 \( cm^{2} \))
\( 24+72 + 24=120 \) \( cm^{2} \)

Filling in the blanks:

• Each triangle: \( A=\frac{1}{2}bh=\frac{1}{2}\times6\times8 = 24 \) \( cm^{2} \) (so the blanks are 6, 24)
• Rectangle: \( A=lw = 9\times8=72 \) \( cm^{2} \) (blanks are 9, 72)
• Trapezoid: \( A = 24+72 + 24=120 \) \( cm^{2} \) (blanks are 24, 72, 24, 120)

Answer:

• Each triangle: \( A=\frac{1}{2}bh=\frac{1}{2}\times\boldsymbol{6}\times8=\boldsymbol{24}\ cm^{2} \)
• Rectangle: \( A = lw=\boldsymbol{9}\times8=\boldsymbol{72}\ cm^{2} \)
• Trapezoid: \( A=\boldsymbol{24}+\boldsymbol{72}+\boldsymbol{24}=\boldsymbol{120}\ cm^{2} \)