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Skate Park and Mural Design

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Skate Park and Mural Design

Split, rearrange, and combine shapes to plan a new skate park.

Surface Plans

A design class is planning a skate park and mural wall. On every coordinate plan, one grid unit represents 1 meter. Complete each shape by drawing a segment from the last labeled vertex back to A (or from F to D in Question 2). Use perpendicular heights, not sloping side lengths.

1.
Triangle ABC is a painted section beside a ramp. Find its area.−8−6−4−224680−6−5−4−3−2−1123456ABC

Area: m²

2.
This triangular mural panel has a vertex beyond the end of its horizontal base. Find the area of triangle DEF.−8−6−4−224680−5−4−3−2−112345DEF

Area: m²

3.
Parallelogram ABCD shows a rubber landing surface. Imagine moving a triangular piece from one end to the other to make a rectangle. What is the area?−8−6−4−224680−5−4−3−2−112345ABCD
Question 3 options
4.
The mural includes rhombus ABCD. Split it along a diagonal into two triangles to find its area.−8−6−4−224680−6−5−4−3−2−1123456ABCD

Area: m²

5.
Trapezoid ABCD is a flat practice zone. Split it into a rectangle and triangles, or into two triangles. Find its area.−8−6−4−224680−6−5−4−3−2−1123456ABCD

Area: m²

Combine and Cut Away

Use the same scale: one grid unit represents 1 meter. Complete each outline by drawing a segment from the last labeled vertex back to A. Find helpful rectangles and triangles inside or around each shape.

6.
Five-sided mural section ABCDE can be split into a rectangle and a triangle. Find its total area.−8−6−4−224680−7−6−5−4−3−2−11234567ABCDE

Total area: m²

7.
L-shaped polygon ABCDEF shows a paved waiting area. Find its area without including the missing upper-right rectangle.−8−6−4−224680−7−6−5−4−3−2−11234567ABCDEF

Area: m²

8.
A corner is cut from an 8 m by 6 m rectangular surface to leave room for a light pole. Polygon ABCDE is the remaining surface. Find its area.−10−8−6−4−22468100−8−7−6−5−4−3−2−112345678ABCDE

Remaining area: m²

9.
Priya splits trapezoid ABCD into a middle rectangle and two right triangles by drawing vertical lines down from C and D. Which expression gives the area in square meters?−10−8−6−4−22468100−5−4−3−2−112345ABCD
Question 9 options
10.
Mateo splits mural section ABCDE into rectangle ABCE and triangle CDE. He writes, “6 × 4 + 6 × 3 = 42 m².” Explain his mistake and give the correct area.−8−6−4−224680−8−7−6−5−4−3−2−112345678ABCDE

Design Decisions

Apply area strategies to the class's final plans. All measurements below are actual lengths, not drawing lengths.

11.
The class will paint two identical triangular panels and one rectangular stripe. Each triangle has a base of 8 m and a perpendicular height of 3 m. The stripe is 10 m long and 2 m wide. The painted regions do not overlap. One can covers 11 m² with one coat.

How many cans are needed for one coat on all three regions? cans

12.
A parallelogram-shaped landing surface has a base of 7.5 m and a perpendicular height of 4 m. Rubber surfacing costs $8 per square meter. There is no extra charge and no material waste.

What is the total cost of the rubber surfacing? $

13.
The class can cover at most 48 m² with a textured finish. These two nonoverlapping zones must be covered first.
Textured Zones
ZoneShapeMeasurements
Rest zoneRectangle6 m long, 5 m wide
Ramp approachTriangleBase 6 m, height 4 m
The triangle's height is perpendicular to its base.

How much area can still receive the finish after both zones are covered? m²

14.
A rectangular mural wall is 8 m wide and 5 m high. A triangular design lies entirely inside the wall. Its base is the full 8 m bottom edge, and its perpendicular height is 3 m. The class paints the triangle blue and the rest of the wall gray. What area will be gray?
Question 14 options