Answer:
The total surface area of the solid is 702 cm² ⇒ answer B
The true statements are m∠WYX = 46° and m∠YWX = 63° ⇒ 1st and 2nd answers
Step-by-step explanation:
* Lets explain the solid figure
- It has one rectangular base of dimensions 10 cm and 14 cm
- It has 4 rectangular side faces , two of dimensions 6 cm and 10 cm
and another two of dimensions 6 cm and 14 cm
- It has 4 triangular faces , two of base 10 cm and height 12 cm and
another two of base 14 cm and height 11 cm
- The total surface area of the solid is the sum of the area of the 9 faces
* Lets find the area of all the faces
# Area of the base
∵ The base is a rectangle
∵ Area of the rectangle = length × width
∵ Length = 14 cm and width = 10 cm
∴ Area of the base = 14 × 10 = 140 cm²
# Area of the four rectangular faces
∵ Length = 10 cm and width = 6 cm
∴ The area of the face with dimensions 10 , 6 = 10 × 6 = 60 cm²
∵ Length = 14 cm and width = 6 cm
∴ The area of the face with dimensions 14 , 6 = 14 × 6 = 84 cm²
# Area of the four triangular faces
∵ Area of a triangle = 1/2 × base × height
∵ The base = 10 cm and the height = 12 cm
∴ The area of the face = 1/2 × 10 × 12 = 60 cm²
∵ The base = 14 cm and the height = 11 cm
∴ The area of the face = 1/2 × 14 × 11 = 77 cm²
∵ The total surface area of the solid = the sum of the areas of 9 faces
∴ TSA = 140 + 2 × 60 + 2 × 84 + 2 × 60 + 2 × 77
∴ TSA = 140 + 120 + 168 + 120 + 154 = 702 cm²
* The total surface area of the solid is 702 cm²
* Lets solve the 2nd part
- WXY is a scalene triangle
- m∠WXY is 71°
- The two sides of the triangle WY and XY exceeded
- The ray WY and the ray XY intersect each other at point Y and
formed vertically opposite angles with measure 46°
∵ Ray WY intersect ray XY at point Y
∴ m∠WYX = 46°
- In Δ WYX
∵ m∠WXY = 71° ⇒ given
∵ m∠WYX = 46° ⇒ proved
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠YWX + m∠WXY + m∠WYX = 180°
∴ m∠YWX + 71° + 46° = 180
∴ m∠YWX + 117° = 180° ⇒ subtract 117 from both sides
∴ m∠YWX = 63°
Lets check the true statements
# m∠WYX = 46° ⇒ true
# m∠YWX = 63° ⇒ true
# m∠WXY = 46° ⇒ not true
# m∠YWX = 46° ⇒ not true
# m∠WYX = 134° ⇒ not true
* The true statements are m∠WYX = 46° and m∠YWX = 63°
