Question

composite shapes practice
name: p: 2
$11×3.5=38.5$

shape name	formula	work it out	area
trapezoid	$a=bh÷2$

shape name	formula	work it out	area

Explanation:

Step1: Split top shape into 2 parts

The top composite shape is a rectangle + trapezoid.

For the rectangle:

Identify dimensions: base $b=11$ in, height $h=3.5$ in.
Formula: $A_{\text{rectangle}} = b \times h$

For the trapezoid:

Identify dimensions: bases $b_1=11$ in, $b_2=15$ in, height $h=3$ in.
Formula: $A_{\text{trapezoid}} = \frac{(b_1 + b_2)}{2} \times h$

Step2: Calculate rectangle area

$A_{\text{rectangle}} = 11 \times 3.5 = 38.5$ $\text{in}^2$

Step3: Calculate trapezoid area

$A_{\text{trapezoid}} = \frac{(11 + 15)}{2} \times 3 = \frac{26}{2} \times 3 = 13 \times 3 = 39$ $\text{in}^2$

Step4: Total area of top shape

$A_{\text{top}} = 38.5 + 39 = 77.5$ $\text{in}^2$

Step5: Split bottom shape into 2 rectangles

The bottom composite shape is two rectangles:

Rectangle 1:

Dimensions: width $5$ cm, height $10$ cm.

Rectangle 2:

Dimensions: width $7$ cm, height $4$ cm.
Formula for each: $A = b \times h$

Step6: Calculate area of bottom rectangles

$A_1 = 5 \times 10 = 50$ $\text{cm}^2$
$A_2 = 7 \times 4 = 28$ $\text{cm}^2$

Step7: Total area of bottom shape

$A_{\text{bottom}} = 50 + 28 = 78$ $\text{cm}^2$

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Top Shape Table Completion:

Shape Name	Formula	Work it Out	Area
Trapezoid	$A = \frac{(b_1 + b_2)}{2} \times h$	$\frac{(11+15)}{2} \times 3$	$39$ $\text{in}^2$

Bottom Shape Table Completion:

Shape Name	Formula	Work it Out	Area
Rectangle 2	$A = b \times h$	$7 \times 4$	$28$ $\text{cm}^2$

Answer:

Total area of top composite shape: $77.5$ $\text{in}^2$
Total area of bottom composite shape: $78$ $\text{cm}^2$