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.
[tex]\text{Area of rectangle}=10\text{ cm}\times 17\text{ cm}[/tex]
[tex]\text{Area of rectangle}=170\text{ cm}^2[/tex]
We know that area of triangle is half the product of base length times height.
[tex]\text{Area of triangle}=\frac{1}{2}\times \text{10 cm}\times 12\text{ cm}[/tex]
[tex]\text{Area of both triangles}=2\times \frac{1}{2}\times \text{10 cm}\times 12\text{ cm}[/tex]
[tex]\text{Area of both triangles}=\text{10 cm}\times 12\text{ cm}[/tex]
[tex]\text{Area of both triangles}=120\text{ cm}^2[/tex]
[tex]\text{Area of banner}=\text{Area of rectangle}+\text{Area of both triangles}[/tex]
[tex]\text{Area of banner}=170\text{ cm}^2+120\text{ cm}^2[/tex]
[tex]\text{Area of banner}=290\text{ cm}^2[/tex]
Therefore, the area of the banner would be 290 square cm.
The total area of the banner is 290 square centimeters and this can be determined by using the formula of the area of rectangle and triangle.
Given :
A banner is composed of two congruent triangles and a rectangle.
The following steps can be used in order to determine the total area of the banner in square centimeters:
Step 1 - First determine the area of the two triangles.
[tex]\rm A' = 2\times 2 \times \dfrac{1}{2}\times 5\times 12[/tex]
Simplify the above expression.
A' = 120 sqaure centimeter
Step 2 - Now, determine the area of the rectangle.
[tex]\rm A" = 17\times 10[/tex]
A" = 170 square centimeter
Step 3 - Now, the total area of the banner in square centimeters is:
A = A' + A"
A = 120 + 170
A = 290 square centimeter
For more information, refer to the link given below:
https://brainly.com/question/1658516
