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 triangle (1):

$b = 3m$, $h=4m$. Then $A_1=\frac{1}{2}\times3\times4 = 6m^{2}$

For triangle (7):

$b = 6in$, $h = 5in$. Then $A_7=\frac{1}{2}\times6\times5=15in^{2}$

Step2: Recall square - area formula

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

Step3: Recall rectangle area formula

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

Step4: Recall parallelogram area formula

The area formula for a parallelogram is $A = bh$, where $b$ is the base and $h$ is the height.

For parallelogram (3):

$b = 9in$, $h = 7in$. Then $A_3=9\times7 = 63in^{2}$

For parallelogram (5):

$b = 5ft$, $h = 9ft$. Then $A_5=5\times9=45ft^{2}$

Step5: 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 trapezoid (4) with $a = 4cm$, $b = 6cm$ and $h = 5cm$, $A_4=\frac{(4 + 6)\times5}{2}=\frac{10\times5}{2}=25cm^{2}$

Step6: For the irregular - shaped (8)

We can split it into a rectangle and a triangle. The rectangle part has length $6cm$ and width $6cm$, and the triangle part has base $6cm$ and height $(11 - 7)=4cm$.
The area of the rectangle is $A_{r}=6\times6 = 36cm^{2}$, the area of the triangle is $A_{t}=\frac{1}{2}\times6\times4=12cm^{2}$. Then $A_8=36 + 12=48cm^{2}$

Answer:

1. $6m^{2}$
2. $25mm^{2}$
3. $63in^{2}$
4. $25cm^{2}$
5. $45ft^{2}$
6. $28yd^{2}$
7. $15in^{2}$
8. $48cm^{2}$