Sure, let’s match each figure with the number of meters in its height based on the given information and solution.
### A. Parallelogram: [tex]\( A = 100 \, m^2 \)[/tex], [tex]\( b = 2 \, m \)[/tex]
- The area of a parallelogram is calculated using the formula [tex]\( A = b \times h \)[/tex], where [tex]\( A \)[/tex] is the area, [tex]\( b \)[/tex] is the base, and [tex]\( h \)[/tex] is the height.
- Given [tex]\( A = 100 \, m^2 \)[/tex] and [tex]\( b = 2 \, m \)[/tex], we can find the height [tex]\( h \)[/tex] as follows:
[tex]\[
h = \frac{A}{b} = \frac{100}{2} = 50 \, m
\][/tex]
- Match: 50 m
### B. Trapezoid: [tex]\( A = 24 \, m^2 \)[/tex], bases [tex]\( 9 \, m \)[/tex] and [tex]\( 3 \, m \)[/tex]
- The area of a trapezoid is calculated using the formula [tex]\( A = \frac{1}{2} (b_1 + b_2) \times h \)[/tex], where [tex]\( A \)[/tex] is the area, [tex]\( b_1 \)[/tex] and [tex]\( b_2 \)[/tex] are the lengths of the two bases, and [tex]\( h \)[/tex] is the height.
- Given [tex]\( A = 24 \, m^2 \)[/tex], [tex]\( b_1 = 9 \, m \)[/tex], and [tex]\( b_2 = 3 \, m \)[/tex], we can find the height [tex]\( h \)[/tex] as follows:
[tex]\[
h = \frac{2A}{b_1 + b_2} = \frac{2 \times 24}{9 + 3} = \frac{48}{12} = 4 \, m
\][/tex]
- Match: 4 m
### C. Parallelogram: [tex]\( A = 8 \, m^2 \)[/tex], [tex]\( b = 4 \, m \)[/tex]
- The area of a parallelogram is calculated using the formula [tex]\( A = b \times h \)[/tex], where [tex]\( A \)[/tex] is the area, [tex]\( b \)[/tex] is the base, and [tex]\( h \)[/tex] is the height.
- Given [tex]\( A = 8 \, m^2 \)[/tex] and [tex]\( b = 4 \, m \)[/tex], we can find the height [tex]\( h \)[/tex] as follows:
[tex]\[
h = \frac{A}{b} = \frac{8}{4} = 2 \, m
\][/tex]
- Match: 2 m
### D. Triangle: [tex]\( A = 20 \, m^2 \)[/tex], [tex]\( b = 5 \, m \)[/tex]
- The area of a triangle is calculated using the formula [tex]\( A = \frac{1}{2} b \times h \)[/tex], where [tex]\( A \)[/tex] is the area, [tex]\( b \)[/tex] is the base, and [tex]\( h \)[/tex] is the height.
- Given [tex]\( A = 20 \, m^2 \)[/tex] and [tex]\( b = 5 \, m \)[/tex], we can find the height [tex]\( h \)[/tex] as follows:
[tex]\[
h = \frac{2A}{b} = \frac{2 \times 20}{5} = \frac{40}{5} = 8 \, m
\][/tex]
- Match: 8 m
### Summary
- A. Parallelogram: [tex]\( A=100 \, m^2 \)[/tex], [tex]\( b=2 \, m \)[/tex] → 50 m
- B. Trapezoid: [tex]\( A=24 \, m^2 \)[/tex], bases [tex]\( 9 \, m \)[/tex] and [tex]\( 3 \, m \)[/tex] → 4 m
- C. Parallelogram: [tex]\( A=8 \, m^2 \)[/tex], [tex]\( b=4 \, m \)[/tex] → 2 m
- D. Triangle: [tex]\( A=20 \, m^2 \)[/tex], [tex]\( b=5 \, m \)[/tex] → 8 m
