Question

find the area of each two - dimensional figure.
① 4 m 3 m area =
② 5 mm area =
③ 7 in 9 in area =
④ 4 cm 5 cm 6 cm area =
⑤ 9 ft 5 ft area =
⑥ 7 yd 4 yd area =
⑦ 5 in 6 in area =
⑧ 11 cm 7 cm 6 cm area =

Explanation:

Step1: Recall triangle area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. For the triangle in (1) with $b = 3m$ and $h=4m$, we have $A_1=\frac{1}{2}\times3\times4$.
$A_1 = 6m^{2}$

Step2: Recall square area formula

The area formula for a square is $A = s^{2}$, where $s$ is the side - length. For the square in (2) with $s = 5mm$, we have $A_2=5\times5$.
$A_2 = 25mm^{2}$

Step3: Recall parallelogram area formula

The area formula for a parallelogram is $A=bh$, where $b$ is the base and $h$ is the height. For the parallelogram in (3) with $b = 9in$ and $h = 7in$, we have $A_3=9\times7$.
$A_3=63in^{2}$

Step4: Recall trapezoid area formula

The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. For the trapezoid in (4) with $a = 4cm$, $b = 6cm$ and $h = 5cm$, we have $A_4=\frac{(4 + 6)\times5}{2}$.
$A_4=\frac{10\times5}{2}=25cm^{2}$

Step5: Recall parallelogram area formula

For the parallelogram in (5) with $b = 5ft$ and $h = 9ft$, using $A=bh$, we get $A_5=5\times9$.
$A_5 = 45ft^{2}$

Step6: Recall rectangle area formula

The area formula for a rectangle is $A = lw$, where $l$ is the length and $w$ is the width. For the rectangle in (6) with $l = 7yd$ and $w = 4yd$, we have $A_6=7\times4$.
$A_6 = 28yd^{2}$

Step7: Recall triangle area formula

For the triangle in (7) with $b = 6in$ and $h = 5in$, using $A=\frac{1}{2}bh$, we get $A_7=\frac{1}{2}\times6\times5$.
$A_7 = 15in^{2}$

Step8: Recall trapezoid area formula

For the trapezoid - like figure in (8), we can split it into a rectangle and a triangle or use the trapezoid formula. Using the trapezoid formula $A=\frac{(a + b)h}{2}$, with $a = 6cm$, $b = 11cm$ and $h = 6cm$, we have $A_8=\frac{(6 + 11)\times6}{2}=\frac{17\times6}{2}=51cm^{2}$

Answer:

1. $6m^{2}$
2. $25mm^{2}$
3. $63in^{2}$
4. $25cm^{2}$
5. $45ft^{2}$
6. $28yd^{2}$
7. $15in^{2}$
8. $51cm^{2}$