Answer:
We can find the total surface area of the figure by taking two triangles and one rectangle at the front and back or by taking trapezium at front at back.
Step-by-step explanation:
Given : Eddie built the ramp shown to train his puppy to do tricks.
We have to find the surface area in two ways.
Since the figure given consist of 3 rectangles at the top and one rectangle at the bottom.
And two triangles and one square at the front and back.
Since area of top and bottom will remain same for both the ways.
Area of rectangle is length × breadth
Area of rectangle 4 is given by,
Area of rectangle 4 = 20 × 24 = 480 inches²
Area of rectangle 5 = 16 × 24 = 384 inches²
Area of rectangle 6 = 20 × 24 = 480 inches²
Area of rectangle at bottom will have length is 48 inches and breadth is 24 inches.
Area of rectangle at bottom = 48 × 24 = 1152 inches²
Total area of top and bottom will be 480 + 480 + 384 + 1152 = 1496 inches²
So we can find the area in two ways by taking two triangles and one rectangle at the front and back or by taking trapezium at front at back
1) two triangles and one square at the front and back
Area of rectangle is length × breadth
Side is 16 inches.
So, Area of square = 16 × 12 = 192 inches²
Area of one triangle =[tex]\frac{1}{2} bh[/tex]
base(b) = 16 and height (h) = 12
Area of one triangle =[tex]\frac{1}{2} \cdot 16\cdot 12 =96[/tex] inches²
Thus area of front is 192 + 96 + 96 = 384 inches²
Thus, total surface area of figure is 1496 inches² + 384 inches²+ 384 inches²= 2264 inches²
2) trapezium at front at back
Area of trapezium = [tex]\frac{1}{2}\cdot (\text{sum of parallel sides})\cdot height[/tex]
Height = 12 inches
Parallel sides are 16 and 48
Area of trapezium = [tex]\frac{1}{2}\cdot (16+48)\cdot 12[/tex]= 384 inches²
Thus, total surface area of figure is 1496 inches² + 384 inches²+ 384 inches²= 2264 inches²
Thus, we can find the total surface area of the figure by taking two triangles and one rectangle at the front and back or by taking trapezium at front at back.
