Answer:
Volume: 85.2 meters^3; Surface area: 123 meters^2
Missing angle: 39 degrees
Step-by-step explanation:
First problem:
Volume
The volume of a rectangular prism, which is what this figure is, is given by the formula: l * w * h (length * width * height).
These values are all given in the figure; for length we have 7.1 m, for width we are given 4 m, and for height we are given 3 m.
Multiply these given values together.
7.1 * 4 * 3 = 85.2
The volume of the figure is 85.2 meters^3.
Surface area
The surface area of a rectangular prism is given by the formula: 2(l * w) + 2(l * h) + 2(w * h). In other words, 2 times length * width, 2 times length * height, and 2 times width times height.
The length of the figure is 7.1 m, the height is 3 m, and the width is 4 m. Substitute these into the formula.
2(7.1 * 4) + 2(7.1 * 3) + 2(4 * 3)
Evaluate and simplify.
123.4 meters^2
Second problem:
A triangle's interior angle measurements add up to 180 degrees, and you are given two out of the three angles.
To find the measure of the third angle, you would add up the known angles and subtract these from 180 degrees to find the measure of the unknown angle.
The equation would look like:
x + 90 + 51 = 180
Combine like terms.
x + 141 = 180
Subtract 141 from both sides of the equation.
x = 39 degrees
The missing angle has a measure equal to 39 degrees.
