Question

A banner is composed of two congruent triangles and a rectangle.

Answer 1

We have been given that a banner is composed of two congruent triangles and a rectangle.  We are asked to find the total area of the banner.

We can see from the diagram that dimensions of rectangle are 10 cm and 17 cm. We know that area of rectangle is length times width.

$\text{Area of rectangle}=10\text{ cm}\times 17\text{ cm}$

$\text{Area of rectangle}=170\text{ cm}^2$

We know that area of triangle is half the product of base length times height.

$\text{Area of triangle}=\frac{1}{2}\times \text{10 cm}\times 12\text{ cm}$

$\text{Area of both triangles}=2\times \frac{1}{2}\times \text{10 cm}\times 12\text{ cm}$

$\text{Area of both triangles}=\text{10 cm}\times 12\text{ cm}$

$\text{Area of both triangles}=120\text{ cm}^2$

$\text{Area of banner}=\text{Area of rectangle}+\text{Area of both triangles}$

$\text{Area of banner}=170\text{ cm}^2+120\text{ cm}^2$

$\text{Area of banner}=290\text{ cm}^2$

Therefore, the area of the banner would be 290 square cm.