Use the image to answer the question.
An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.
What is the length of AB?(1 point)
There is no way to determine the length of AB based on the information provided. The length of AB is not directly given or able to be calculated from the dimensions provided.
ok... Kym’s sawhorse is 39 inches tall, 27 inches long, and 19 inches wide. Its diagonal measurement, or the hypotenuse, is 40.14 inches. What is its total surface area? Round your answer to the nearest hundredth.
We can start by using the Pythagorean theorem to find the height of the sawhorse in relation to its length and width:
h^2 = l^2 + w^2
h^2 = 27^2 + 19^2
h^2 = 1090
h = 33.05 inches (rounded to the nearest hundredth)
Now we can calculate the surface area by adding up the areas of each face. The sawhorse has two pairs of identical rectangular faces (front/back and sides):
Front/back face area = h x l = 33.05 x 27 = 891.35 sq in
Side face area = h x w = 33.05 x 19 = 627.95 sq in
The sawhorse also has a rectangular top face:
Top face area = l x w = 27 x 19 = 513 sq in
To find the area of the triangular faces, we can use the formula for the area of a triangle (1/2 base x height) and the Pythagorean theorem to find the height of each triangle:
Triangle height^2 = hypotenuse^2 - base^2
Triangle height^2 = 40.14^2 - 19^2
Triangle height^2 = 1281.0396
Triangle height = 35.79 inches (rounded to the nearest hundredth)
Each triangular face has a base of 27 inches and a height of 35.79 inches, so their combined area is:
2 x (1/2 x 27 x 35.79) = 767.37 sq in
Adding up the areas of all the faces, we get:
891.35 + 891.35 + 627.95 + 627.95 + 513 + 767.37 = 4310.97 sq in
So the total surface area of the sawhorse is approximately 4310.97 square inches (rounded to the nearest hundredth).
Based on the given information, we can determine the length of AB by examining the dimensions of the rectangles and triangles in the illustration.
Since the second rectangle in the middle is labeled as 3 inches in length and 2 inches in width, we can deduce that AB is equal to the width of this rectangle, which is 2 inches. Therefore, the length of AB is 2 inches.