Question

what is the total area of the shape?4 cm3 cm10 cm3 cm(not drawn to scale)a $35\\ \text{cm}^2$b $100\\ \text{cm}^2$c $70\\ \text{cm}^2$d $50\\ \text{cm}^2$

Explanation:

Step1: Calculate area of rectangle

The rectangle has length $10$ cm and width $4$ cm. Area of a rectangle is $\text{length} \times \text{width}$.
$\text{Area}_{\text{rectangle}} = 10 \times 4 = 40$ $\text{cm}^2$

Step2: Calculate area of one triangle

Each triangle has base $10$ cm and height $3$ cm. Area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
$\text{Area}_{\text{one triangle}} = \frac{1}{2} \times 10 \times 3 = 15$ $\text{cm}^2$

Step3: Calculate total area of two triangles

There are two identical triangles, so multiply the area of one triangle by 2.
$\text{Area}_{\text{two triangles}} = 15 \times 2 = 30$ $\text{cm}^2$

Step4: Sum all areas to get total area

Add the area of the rectangle and the total area of the two triangles.
$\text{Total Area} = 40 + 30 = 70$ $\text{cm}^2$

Answer:

C. $70 \text{ cm}^2$