Question

Eddie built the ramp shown to train his puppy to do tricks. Describe two ways to find the surface area of the ramp.

Answer 1

multiply all sides add all sides then divide by how many #'s there are

Answer 2

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.

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 =
`(1)/(2) bh`

base(b) = 16 and height (h) = 12

Area of one triangle =
`(1)/(2) \cdot 16\cdot 12 =96` 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 =
`(1)/(2)\cdot (\text{sum of parallel sides})\cdot height`

Height = 12 inches

Parallel sides are 16 and 48

Area of trapezium =
`(1)/(2)\cdot (16+48)\cdot 12`= 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.